Torsion Group Research Articles

Apoptotic balance during testicular detorsion after one hour induced torsion in rats.

Testicular torsion (TT) is an emergency complication that leads to oxidative stress and adversely affects spermatogenesis. Although immediate treatment consists of testicular detorsion (TD) to reverse TT-induced ischemia, mechanisms underlying recovery have yet to be fully understood. The current study aimed to investigate TD effects after a one-hour experimental TT by evaluating testicular antioxidant status and apoptosis-related proteins. Forty male Wistar rats were submitted to TT by testicular rotation, for one hour. Following TT, 32 rats were submitted to TD for 1, 2, 4, and 8h (N=8/group), the other 8 rats euthanized as TT-only. For controls, 8 rats were sham-operated. Testicular tissues were aseptically dissected for biochemical, histopathological, and immunohistochemistry analyses. The TD groups, especially after 4h of TD, exhibited diminished MDA and increased TAC and GPX levels in testicular tissue. Levels of p53 and Caspase-3 were down-regulated in T1D4 and T1D8groups versus torsion group. Bcl-2 was increased in T1D4 and T1D8groups compared to the TT group. Moreover, spermatogenesis was recovered in T1D4 and T1D8groups compared to the TT group. It can be concluded that after 1h TT in rats, at least 4h post-TD is needed for testicular tissue to initiate recovery.

Nil-generated algebras and group algebras whose units satisfy a Laurent polynomial identity

Let A be an algebra whose group of units U(A) satisfies a Laurent polynomial identity (LPI). We establish conditions on LPIs in such a way that nil-generated algebras and group algebras with torsion groups over infinite fields in characteristic p > 0 have nonmatrix identities. We also determine, in the context of group algebras with arbitrary LPI for the group of units, the existence of polynomial identities.

Recurrent Ovarian Torsion and Fixation – Risk Factors and Predictors for Treatment Outcome

<h3>Study Objective</h3> Identifying risk factors for recurrent ovarian torsion and evaluation of the efficacy of ovarian fixation techniques. <h3>Design</h3> Retrospective cohort study. <h3>Setting</h3> Tertiary-care medical center. <h3>Patients or Participants</h3> Seventy-nine women with recurrent ovarian torsion (study group) were matched with 158 women with a single episode of ovarian torsion (control) during the same year of their first episode. <h3>Interventions</h3> Demographic data, clinical and surgical characteristics were retrieved between the years 2001-2020. In order to identify risk factors for recurrent ovarian torsion, the first episode of ovarian torsion in the study group was compared to the only episode of the control group. A second analysis was performed between women with ovarian fixation (success and failure). <h3>Measurements and Main Results</h3> Women with recurrent torsion were significantly younger and the percentage of premenarchal women was significantly higher (25.6±8.6 vs. 30.6±7.1, P<0.001, and 10% vs. 0.6%, P<0.001, respectively). Fertility treatment and pregnancy were significantly more common in the control group (37.7% vs. 23.6%, P=0.03, and 36.4% vs. 20.7%, P=0.01, respectively). Ovarian pathology was significantly more common in the control group (89.0% vs. 38.1%, P<0.001), whereas the number of ovarian twists was significantly higher in the recurrent torsion group (2.6±0.01 vs. 2.0±0.1, P=0.04). Ovarian fixation was performed in 63 women (79.7%) of the study group with an overall success rate of 71%. Long duration of pain before admission was associated with ovarian fixation failure (37.5±6.3 hours vs. 11.7±6.0, P=0.003). Ovarian fixation during pregnancy was shown to be safe with low failure rate (6% vs. 36%, P=0.03). None of the fixation procedures was shown to be superior to the others in terms of success. <h3>Conclusion</h3> Recurrent ovarian torsion is more common in young premenarchal women. Ovarian fixation is a safe procedure with a 70% success rate. We found no advantage in one fixation techniques over the others.

Elements of uniformly bounded word-length in groups

We study a characteristic subgroup of finitely generated groups, consisting of elements with uniform upper bound for word-lengths. For a group G , we denote this subgroup by G_\mathrm{bound} . We give sufficient criteria for triviality and finiteness of G_\mathrm{bound} . We prove that if G is virtually abelian then G_\mathrm{bound} is finite. In contrast with numerous examples where G_\mathrm{bound} is trivial, we show that for every finite group A , there exists an infinite group G with G_\mathrm{bound}=A . This group G can be chosen among torsion groups. We also study the group G_\mathrm{bound}(d) of elements with uniformly bounded word-lengths for generating sets of cardinality less than d .

Torsion groups of Mordell curves over cubic and sextic fields

In this paper, we classify torsion groups of rational Mordell curves explicitly over cubic fields as well as over sextic fields. Also, we classify torsion groups of Mordell curves over cubic fields and for Mordell curves over sextic fields, we produce all possible torsion groups.

Effects of Rosmarinus officinalis on orchitis following spermatic cord torsion-detorsion in male mice with emphasis on anti-inflammatory and antioxidant properties.

Orchitis as inflammation of testis occurs following traumatic injuries such as testicular torsion leading to high levels of oxidative stress and inflammation. Rosmarinus officinalis is a herb with anti-inflammatory and antioxidant properties. This study assessed therapeutic effects of rosemary following testicular torsion. A total of 36 male mice were categorised; control, torsion, rosemary (100 and 200mg/kg) and torsion+rosemary groups. Torsion was induced surgically, and rosemary was gavaged. Total antioxidant capacity of extract was approved by Ferric Reducing Ability of Plasma. Malondialdehyde and Griess protocols were hired to assess oxidative stress. Finally, sperm parameters and testosterone levels were analysed. Immunofluorescent (of Tumour Necrosis Factor Alpha), hematoxylin and eosin stainings and expression of inflammatory genes (Interleukin-1α, Interleukin-1β, Interferon-γ) were also assessed. Data were analysed using SPSS (v. 19), and graphs were drawn by GraphPad Prism (v. 9). Significantly (p<.05), oxidative stress indices and inflammatory genes expression were increased in torsion group, and total antioxidant capacity was increased in rosemary groups. In torsion+rosemary groups, total antioxidant capacity, sperm parameters and testosterone levels were increased, and inflammatory gene expression decreased significantly (p<.05). Rosemary with anti-inflammatory and antioxidant properties accelerates testicular healing in torsion cases, especially in therapeutic dose of 200mg/kg.

$${{\mathbb {Q}}}$$-curves over odd degree number fields

By reformulating and extending results of Elkies, we prove some results on \({{\mathbb {Q}}}\)-curves over number fields of odd degree. We show that, over such fields, the only prime isogeny degrees \(\ell \) that a \({{\mathbb {Q}}}\)-curve without CM may have are those degrees that are already possible over \({{\mathbb {Q}}}\) itself (in particular, \(\ell \le 37\)), and we show the existence of a bound on the degrees of cyclic isogenies between \({{\mathbb {Q}}}\)-curves depending only on the degree of the field. We also prove that the only possible torsion groups of \({{\mathbb {Q}}}\)-curves over number fields of degree not divisible by a prime \(\ell \le 7\) are the 15 groups that appear as torsion groups of elliptic curves over \({{\mathbb {Q}}}\). Complementing these theoretical results, we give an algorithm for establishing whether any given elliptic curve E is a \({{\mathbb {Q}}}\)-curve, that involves working only over \({{\mathbb {Q}}}(j(E))\).

Constructing cubic curves with involutions

In 1888, Heinrich Schroeter provided a ruler construction for points on cubic curves based on line involutions. Using Chasles’ Theorem and the terminology of elliptic curves, we give a simple proof of Schroeter’s construction. In addition, we show how to construct tangents and additional points on the curve using another ruler construction which is also based on line involutions. As an application of Schroeter’s construction we provide a new parametrisation of elliptic curves with torsion group mathbb {Z}/2mathbb {Z}times mathbb {Z}/8mathbb {Z} and give some configurations with all their points on a cubic curve.

Elliptic curves with torsion groups $${ \mathbb {Z}}/ 8 {\mathbb {Z} } $$ and $${ \mathbb {Z}}/ 2 {\mathbb {Z}} \times {\mathbb {Z}}/ 6 {\mathbb {Z}}$$

In this paper, we present details of seven elliptic curves over $${\mathbb {Q}}(u)$$ with rank 2 and torsion group $${\mathbb {Z}}/8{\mathbb {Z}}$$ and five curves over $${\mathbb {Q}}(u)$$ with rank 2 and torsion group $${\mathbb {Z}}/2{\mathbb {Z}}\times {\mathbb {Z}}/6{\mathbb {Z}}$$ . We also exhibit some particular examples of curves with high rank over $${\mathbb {Q}}$$ by specialization of the parameter. We present several sets of infinitely many elliptic curves in both torsion groups and rank at least 3 parametrized by elliptic curves having positive rank. In some of these sets we have performed calculations about the distribution of the root number. This has relation with recent heuristics concerning the rank bound for elliptic curves by Park, Poonen, Voight and Wood.

Effects of vitamin B12 on rat ovary with ischemia-reperfusion injury

ABSTRACT We investigated the histopathological and biochemical effects of vitamin B12 on ischemia-reperfusion (I-R) injury using a rat ovarian torsion-detorsion model. We used four groups of female Wistar albino rats. Group 1 (sham group): both ovaries were removed. Group 2 (torsion group): ovarian torsion was established. Group 3 (torsion-detorsion group) perfusion was retored after ischemia for 2 h. Group 4 (torsion-detorsion-vitamin B12 group): after 2 h ovarian torsion, perfusion was re-established and 4 mg/kg vitamin B12 was administered for 2 h. Follicular degeneration, vascular congestion, hemorrhage, edema and infiltration were evaluated histologically. Tissue damage was decreased in group 4 compared to groups 2 and 3. Total antioxidant status TAS), total oxidant status (TOS) and malondialdehyde (MDA) level were measured. The values for TOS and MDA for groups 1 and 4 were similar. We found a significant increase in MDA and TOS levels in group 3 compared to group 2. MDA and TAS levels decreased and TOS levels were increased in group 4 compared to groups 2 and 3. MDA, TAS and TOS values were increased in groups 2 and 3 compared to group 1. We found that vitamin B12 reduced I-R damage in the rat ovary.

Cross-link between mitochondrial-dependent apoptosis and cell cycle checkpoint proteins after experimental torsion and detorsion in rats.

The current study assessed the cross-link between mitochondria-related apoptosis and cell cycle machinery systems during ischemia and reperfusion in a rat model of testicular torsion and detorsion. The Wistar male rats were divided into control, 1h, 2h, 4h and 8h testicular torsion-induced, and 1h, 2h, 4h and 8h testicular detorsion-induced groups. The Johnson's score was analyzed. The mRNA and protein contents of Bcl-2, Bax, Caspase-3, Cyclin D1, Cdk4, P21 and P53 were investigated by sqRT-PCR and immunohistochemical staining, respectively. The apoptosis index was analyzed by TUNEL staining. The mRNA levels of bax, p53, p21 and cyclin D1 were increased, and the mRNA levels of bcl-2 and cdk4 were decreased in torsion and reperfusion-induced groups, time-dependently. The caspase-3 mRNA was increased in torsion-induced and diminished in detorsion-induced groups. A time-dependent reduction in Bcl-2+, Caspase-3+, Cyclin D1+, Cdk4+ and P53+ and increment in P21+ cells distribution per mm2 of tissue were revealed after torsion and detorsion. The apoptosis index was increased after torsion and decreased after detorsion. In conclusion, torsion-induced severe DNA damage stimulates the cyclin D1, p53 and p21 mRNA expression while more than 8h is needed to reveal them as protein content in testicular tissue. About detorsion, decreased Cyclin D1 and Cdk4 proteins and the P53-induced transcriptional effect on p21 expression, stimulates the p21 bind to cdk4 and consequent failure in Cyclin D1/Cdk4 complex formation. This situation in association with apoptotic genes results in spermatogenesis failure.

Algorithmic complexity of Greenberg’s conjecture

Let k be a totally real number field and p a prime. We show that the “complexity” of Greenberg’s conjecture ( $$\lambda = \mu = 0$$ ) is governed (under Leopoldt’s conjecture) by the finite torsion group $${{\mathscr {T}}}_k$$ of the Galois group of the maximal abelian p-ramified pro-p-extension of k, by means of images, in $${{\mathscr {T}}}_k$$ , of ideal norms from the layers $$k_n$$ of the cyclotomic tower (Theorem 4.2). These images are obtained via the algorithm computing, by “unscrewing”, the p-class group of $$k_n$$ . Conjecture 4.3 of equidistribution of these images would show that the number of steps $$b_n$$ of the algorithms is bounded as $$n \rightarrow \infty $$ , so that (Theorem 3.3) Greenberg’s conjecture, hopeless within the sole framework of Iwasawa’s theory, would hold true “with probability 1”.

Pairing pythagorean pairs

A pair (a,b) of positive integers is a pythagorean pair if a2+b2=□ (i.e., a2+b2 is a square). A pythagorean pair (a,b) is called a double-pythapotent pair if there is another pythagorean pair (k,l) such that (ak,bl) is a pythagorean pair, and it is called a quadratic pythapotent pair if there is another pythagorean pair (k,l) which is not a multiple of (a,b), such that (a2k,b2l) is a pythagorean pair. To each pythagorean pair (a,b) we assign an elliptic curve Γa,b with torsion group Z/2Z×Z/4Z, such that Γa,b has positive rank over Q if and only if (a,b) is a double-pythapotent pair. Similarly, to each pythagorean pair (a,b) we assign an elliptic curve Γa2,b2 with torsion group Z/2Z×Z/8Z, such that Γa2,b2 has positive rank over Q if and only if (a,b) is a quadratic pythapotent pair. Moreover, in the later case we obtain that every elliptic curve Γ with torsion group Z/2Z×Z/8Z is isomorphic to a curve of the form Γa2,b2, where (a,b) is a pythagorean pair. As a side-result we get that if (a,b) is a double-pythapotent pair, then there are infinitely many pythagorean pairs (k,l), not multiples of each other, such that (ak,bl) is a pythagorean pair; the analogous result holds for quadratic pythapotent pairs.

A NOTE ON GROUP RINGS WITH TRIVIAL UNITS

AbstractLet R be a ring with identity of characteristic two and G a nontrivial torsion group. We show that if the units in the group ring $RG$ are all trivial, then G must be cyclic of order two or three. We also consider the case where R is a commutative ring with identity of odd prime characteristic and G is a nontrivial locally finite group. We show that in this case, if the units in $RG$ are all trivial, then G must be cyclic of order two. These results improve on a result of Herman et al. [‘Trivial units for group rings with G-adapted coefficient rings’, Canad. Math. Bull.48(1) (2005), 80–89].

Association Between Orientation and Magnitude of Femoral Torsion and Propensity for Clinically Meaningful Improvement After Hip Arthroscopy for Femoroacetabular Impingement Syndrome: A Computed Tomography Analysis

Background: Femoral torsion imaging measurements and classifications are heterogeneous throughout the literature, and the influence of femoral torsion on clinically meaningful outcome improvement after hip arthroscopy for femoroacetabular impingement syndrome (FAIS) has not been well studied. Purpose: To (1) perform a computed tomography (CT)–based analysis to quantify femoral torsion in patients with FAIS and (2) explore the relationship between the orientation and magnitude of femoral torsion and the propensity for clinically meaningful outcome improvement after hip arthroscopy. Study Design: Cohort study; Level of evidence, 3. Methods: Consecutive patients who underwent hip arthroscopy for FAIS between January 2012 and April 2018 were identified. Inclusion criteria were the presence of preoperative CT imaging with transcondylar slices of the knee and minimum 2-year outcome measures. Exclusion criteria were revision hip arthroscopy, Tönnis grade >1, congenital hip condition, hip dysplasia (lateral center-edge angle <20°), and concomitant gluteus medius or minimus repair. Torsion groups were defined as severe retrotorsion (SR; <0°), moderate retrotorsion (MR; 0°-5°), normal torsion (N; 5°-20°), moderate antetorsion (MA; 20°-25°), and severe antetorsion of antetorsion (SA; >25°). Treatment did not differ based on femoral torsion. Patient characteristics and clinical outcomes were analyzed, including the Hip Outcome Score–Activities of Daily Living (HOS-ADL), Hip Outcome Score–Sports Subscale (HOS-SS), modified Harris Hip Score (mHHS), international Hip Outcome Tool (iHOT-12), visual analog scale (VAS) for pain, and VAS for satisfaction. Achievement of the minimal clinically important difference (MCID) and patient acceptable symptom state (PASS) by torsion stratification was analyzed using the chi-square test. Inter- and intrarater reliabilities for CT measurements were 0.980 (P < .001) and 0.974 (P < .001), respectively. Results: The study included 573 patients with a mean ± SD age and body mass index of 32.6 ± 11.8 years and 25.6 ± 10.6, respectively. The mean ± SD femoral torsion for the study population was 12.3°± 9.3°. After stratification, the number of patients within each group and the mean ± SD torsion for each group were as follows: SR (n = 36; –6.5°± 7.1°), MR (n = 80; 2.8°± 1.4°), N (n = 346; 12.3°± 4.1°), MA (n = 64; 22.2°± 1.4°), and SA (n = 47; 30.3°± 3.7°). No significant differences in age, body mass index, sex, tobacco use, workers’ compensation status, or participation in physical activity were observed at baseline. No significant differences were seen in pre- and postoperative VAS pain, mHHS, HOS-ADL, HOS-SS, iHOT-12, or postoperative VAS satisfaction among the cohorts. Furthermore, no statistically significant differences were found in the proportion of patients who achieved the MCID or the PASS for any outcome among the groups. Conclusion: The orientation and severity of femoral torsion at the time of hip arthroscopy for FAIS did not influence the propensity for clinically significant outcome improvement.

Every $BT_1$ group scheme appears in a Jacobian

Let $p$ be a prime number and let $k$ be an algebraically closed field of characteristic $p$. A $BT_1$ group scheme over $k$ is a finite commutative group scheme which arises as the kernel of $p$ on a $p$-divisible (Barsotti--Tate) group. Our main result is that every $BT_1$ scheme group over $k$ occurs as a direct factor of the $p$-torsion group scheme of the Jacobian of an explicit curve defined over $\mathbb{F}_p$. We also treat a variant with polarizations. Our main tools are the Kraft classification of $BT_1$ group schemes, a theorem of Oda, and a combinatorial description of the de Rham cohomology of Fermat curves.

Tate–Shafarevich groups in the cyclotomic [formula omitted]-extension and Weber's class number problem

Let K=Q(N) be the Nth layer in the cyclotomic Zˆ-extension. Many authors (Aoki, Fukuda, Horie, Ichimura, Inatomi, Komatsu, Miller, Morisawa, Nakajima, Okazaki, Washington,…) prove results on the p-class groups CK. We enlarge “Weber's problem” to the Tate–Shafarevich groups IIIK1≃CKSp[p] and IIIK2 having same p-rank as the more easily computable torsion group, TK, of the Galois group of the maximal abelian p-ramified pro-p-extension of K; but TK is often non-trivial, which raises questions for class groups since ▪, where RK is the normalized p-adic regulator. We give a new method testing TK≠1 (Theorem 4.6, Table in Appendix A.7) and characterize the fields K1=KQ(p) with CK1≠1 (Main Theorem 1.1 affirming, for short, that CK1≠1 if and only if p totally splits in K and TK≠1); this highlights the analytical results and justifies the eight known examples. All PARI/GP programs are given for further investigations.

The effect of intratesticular dexpanthenol on experimentally-induced testicular ischaemia/reperfusion injury

Testis torsion is a urological emergency and a serious situation that may cause testis atrophy, testicular dysfunction and infertility due to ischaemia/reperfusion(I/R) injury even with early intervention. To assess the protective effect of dexpanthenol administered intratesticular after detorsion against testis I/R injury. Twenty-seven rats were randomly divided into 3 groups containing 9 rats each. The 1st group comprised the sham group with no procedure performed. The 2nd group had only torsion applied, while the 3rd group had torsion+dexpanthenol applied. Rats had 720° clockwise rotation applied to the left testis. After 2h of ischaemia, testes were de-torsioned and the dexpanthenol group had 500mg/kg dexpanthenol administered intratesticular after detorsion. After 4h of reperfusion, rats had blood samples taken and orchiectomy was performed for histologic assessment. A significant difference was detected in all parameters [necrosis(p:<0.001), Cosentino grade (p<0.001), congestion (p:0.005), fibrosis (p:<0.001), interstitial oedema (p:0.017), JTBS score (p:<0.001), apoptosis (p<0.001) and testosterone levels (p:0.006)] when the sham, torsion, and torsion+dexpanthenol groups were compared. Significant differences were observed for fibrosis (p:0.010), Cosentino score (p<0.001), JTBS score (p:<0.001), apoptosis (p:0.001) and total testosterone levels (p:0.013) when torsion and torsion+dexpanthenol groups were compared. The torsion+dexpanthenol group was identified to have more preservation of testis function observed histologically and hormonally compared to the torsion group. Dexpanthenol is used in many areas due to both epithelizing and antioxidant effects and lack of clear side effects. In spite of use of many chemical and biological agents to protect against testis I/R injury, none have entered routine use. This study showed that dexpanthenol, which can be easily injected intratesticular during detorsion surgery, has protective effect against histological and functional injury that may develop linked to testis I/R injury. The main limitations of the study are short duration of follow-up due to being a rat experiment and lack of comparison of lipid peroxidation products. This study identified that dexpanthenol with clinically easy use by intratesticular injection after detorsion during surgery had a protective effect against histological and functional injury that will develop linked to I/R injury in the testis.

Clinical-ultrasound and clinical-morphological characteristics of adnexal torsion in girls and adolescents

Clinical-ultrasound and clinical-morphological characteristics of adnexal torsion to the improvement of early diagnosis and development of optimal ways of organ-preserving surgical tactics of treatment have been determined. An analysis was carried out of 71 patients with adnexal torsion (group 1– 30 girls of 2–12 years, group 2 – 41 adolescents of 13–17 years). The main clinical signs of adnexal torsion were nonspecific and similar to the well-known clinic of acute abdomen. Ultrasound examination with color doppler mapping (CDM) allowed to suspect adnexal torsion in 44 (62 %) patients. The main echographic features of adnexal torsion were: ovarian enlargement, non-typical location and a change in the structure of ovary, the presence of a free liquid in the cavity of a small pelvis or in the abdominal cavity, «a symptom of springs» (a twisted vascular leg), a decrease or absence of blood flow in CDM. The torsion of intact uterine appendages is installed in 29 patients (twice as often in group 1). In 42 cases were detected the torsion of the uterine appendages, compromised by the presence of tumors and tumor-like formations (twice as often in group 2). In both groups, 36 (50.7 %) organ-preserving and 35 (49.3 %) radical operations were carried out. According to the results of morphological examination of the removed tissues, the following data were obtained: follicular cysts – 15, paratubal cysts – 8, corpus luteum cysts – 8, teratomas – 5, serous cystadenomas – 2, mucinous cystadenoma – 1, paraovarian cysts – 3. Differential diagnosis of adnexal torsion in girls and adolescents should include a thorough collection of anamnestic data, taking into account the features of the clinical course of the disease, the results of a comprehensive examination with an assessment of ultrasound data from CDM, computer and magnetic resonance imaging, which will contribute to the advanced adequate selection of tactics of urgent gynecological intervention. The method of choice for the treatment of adnexal torsion is a minimally invasive surgical intervention – a laparoscopy with organ-preserving operations. Keywords: adnexal torsion, girls, ultrasound and morphological characteristics.

Swampland cobordism conjecture and non-Abelian duality groups

We study the cobordism conjecture of McNamara and Vafa which asserts that the bordism group of quantum gravity is trivial. In the context of type IIB string theory compactified on a circle, this predicts the presence of D7-branes. On the other hand, the non-Abelian structure of the IIB duality group $SL(2,\mathbb{Z})$ implies the existence of additional $[p,q]$ 7-branes. We find that this additional information is instead captured by the space of closed paths on the moduli space of elliptic curves parameterizing distinct values of the type IIB axio-dilaton. This description allows to recover the full structure of non-Abelian braid statistics for 7-branes. Combining the cobordism conjecture with an earlier Swampland conjecture by Ooguri and Vafa, we argue that only certain congruence subgroups $\mathrm{\ensuremath{\Gamma}}\ensuremath{\subset}SL(2,\mathbb{Z})$ specifying genus zero modular curves can appear in 8D F-theory vacua. This leads to a successful prediction for the allowed Mordell--Weil torsion groups for 8D F-theory vacua.