Torsion Group Research Articles

High-rank elliptic curves with given torsion group and some applications

High-rank elliptic curves with given torsion group and some applications

Automorphisms of Mackey groups

We consider total subspaces of linear functionals on an infinite-dimensional vector space and the related Mackey algebras and groups. We outline the description of automorphisms of Mackey groups SL∞(V|W), O∞(f), and SU∞(f) over fields of characteristics not equal to 2, 3. Moreover, the paper explores the relationship between field automorphisms and automorphisms of the aforementioned groups. J.Hall proved that infinite simple finitary torsion groups are the alternating groups on infinite sets or Mackey groups over a field, which is an algebraic extension of a finite field. J.Schreier and S.Ulam described automorphisms of infinite alternating groups. With the description of automorphisms of finitary Mackey groups and special finitary unitary Mackey groups we finish classification of automorphisms of all infinite simple finitary torsion groups over fields of characteristics not equal to 2, 3. The proof is based of description of automorphisms of elementary linear groups over associative rings that due to I.Golubchik, A.Mikhalev and E.Zelmanov.

Pregnancy-Associated Ovarian Torsion - a Single-Center Case-Control Study.

The etiology of OT is largely unknown. Any predisposition to rotation of the infundibulopelvic ligament and utero-ovarian ligament should be considered a possible etiology. Information with respect to ovarian torsion (OT) among pregnant is underreported and based on small studies. We aim to compare characteristics of confirmed OT to laparoscopies performed for the indication of suspected OT, in which no OT was found among pregnant women. This is a retrospective case-control study. We included pregnant women who underwent laparoscopy for a suspected OT between March 2011 and August 2020. Pregnant women with confirmed OT (torsion group) were compared to those without (no torsion group). There were 169 women with suspected OT. OT was confirmed in 140 (82.8%) women. There was higher proportion of assisted reproductive technology (ART) gestation in the torsion group [76 (54.3%) vs. 5 (17.2%), p < 0.001]. The rate of pregnant approaching evaluation within 8h of symptoms onset was higher in the torsion group [57 (40.7%) vs. 2 (6.9%), p < 0.001]. The mean visual analogue score (VAS) was higher in the torsion group (8.5 vs. 7.1, p = 0.002). The mean pulse was lower in the torsion group (79 vs. 88bpm, p < 0.001). From sonographic characteristics examined, the following was higher in the torsion group; mean maximal size of the ovary (70mm in the torsion group vs. 54mm in the no torsion group, p = 0.011). In a multivariable logistic regression analysis, number of hours of symptoms was negatively associated with AT [aOR, 95% CI 0.95 (0.91-0.98)] and pulse was negatively associated with OT [aOR, 95% CI 0.78 (0.63-0.95)]. Among the 29 cases in which no OT was found during laparoscopy, the following findings were noted: 16 (55.2%) no abnormality at all, 5 (17.2%) functional ovarian cyst, 2 (6.9%) mature teratoma and 6 cases of peritoneal adhesions (20.7%). The time from pain onset to approaching evaluation and women's pulse should be considered and acknowledged in the evaluation of OT during pregnancy.

The average analytic rank of elliptic curves with prescribed torsion

We show that average analytic rank of elliptic curves with prescribed torsion $G$ is bounded for every torsion group $G$ under GRH for elliptic curve $L$-functions.

Experimental study of the torsional effect for yarn break load test of polymeric multifilaments

Polymeric multifilaments have gained a significant interest in recent decades. In the studies of mechanical characteristics, although there are different types of tests, such as rupture, abrasion, creep, impact and fatigue, it can be said that the main mechanical characterisation is the tensile rupture strength (Yarn Break Load, YBL), which also serves as a parameter for other tests. The objective of this work is to evaluate the results of breaking strength under different torsional conditions in polymeric multifilaments and to determine optimal twists for failures. The test were carried out with the following materials: polyamide, polyester, and high modulus polyethylene (HMPE), and for torsional conditions: 0, 20, 40, 60, 120, 240, and 480 turns per metre. As a result, for these torsion groups, curves were obtained for the three materials that present an optimal point of maximum rupture value, which was also experimentally proven. The twist that optimises the breaking strength of HMPE is 38 turns per metre, 56 turns per metre for polyester, and 95 turns per metre for polyamide. The twist groups that exceed the optimal torsion have a deleterious effect on the material, where the multifilament ceases to be homogeneous and starts to create an excessive "spring effect". The results found differ from the recommendation of the standard that regulates the YBL test, and thus, a relationship is built between groups of optimal torsion and linear density that provides evidence that the increase in linear density causes the optimal torsion for rupture to also increase, while the standard places a condition of 30 turns per metre for linear densities greater than 2200 dtex, and 60 turns per metre for linear densities less than 2200 dtex. In addition to optimal torsion values, this conclusion is paramount, the test procedure makes a general recommendation that does not optimise the breaking strength.

The Impact of Chrysin on The Folliculogenesis and Ovarian Apoptosis in Ischemia-Reperfusion Injury in The Rat Model.

The ovarian Ischemia/reperfusion is one of the gynecological emergency concerns that may lead to the ovary damage and folliculogenesis. The present research aimed to evaluate the impact of the Chrysin (CH) on the ischemia-reperfusion (I/R) injury in the rat model. In this experimental research, 48 adult female rats, 8 weeks age and 180-200 g weight, have been categorized into 6 equal groups (n=8) including one sham and 5 ovarian torsion groups (OT+CH groups) that received different treatments. Each group has been treated 30 min before detorsion with gavage of CH or normal saline for 1 week and pregnant mare serum gonadotropin (PMSG) has been injected on the day 5 for initiating folliculogenesis. Finally, bio-chemical, molecular, histopathological, apoptotic and hormonal evaluations were performed. The anti-oxidant enzyme, superoxide dismutase and glutathione peroxidase, ameliorated in the ovarian tissues of the OT+CH groups in comparison with the OT group (P<0.001). Moreover, the level of serum Luteinizing hormone considerably declined and estradiol level (P<0.001), partly enhanced in the rats treated with CH in comparison with the ones in the OT group (P<0.05). In addition, histopathological scores of the OT+CH groups ameliorated in comparison with the OT group scores (P<0.05). Furthermore, the expression Caspase-3 and Bax genes were significantly increased while the expression of Bcl-2 was notably decreased in the OT group in comparison with the sham group (P<0.05). Here, it seems that CH is possibly beneficial for the protection of ovaries against reperfusion injury and ischemia.

The protective effect of erythropoietin on ischemia- reperfusion injury caused by ovarian torsion-detorsion in the experimental rat model

ABSTRACT Ovarian torsion is one of the most dangerous gynecological emergencies requiring surgery. A total of 50%–90% ovarian torsion cases are caused by physiological cysts, endometriosis, and other benign or malignant ovarian neoplasms. The aim of the study was to investigate the effects of erythropoietin (EPO) treatment on ischemia/reperfusion (IR) injury caused by ovarian torsion/detorsion (T/D) injury. Thirty female Wistar albino rats were divided into five groups as follows: Group I: Control; Group II: Torsion (T); Group III: Torsion/Detorsion(T/D); Group IV: Torsion/Detorsion (T/D) + EPO; Group V: EPO. Sections of the ovaries were evaluated for histopathological changes with hematoxylin and eosin stain, a immunohistochemical assay for caspase 3 expression, and the TUNEL assay for apoptosis. Ovarian sections from torsion/detorsion and torsion groups showed more hemorrhage, vascular congestion, edema, degenerative granulosa, and stromal cells. Fewer histopathological changes were found in EPO and T/D + EPO groups. Caspase 3 and TUNEL positive cells were significantly increased in the torsion/detorsion group as compared with the other groups (p < 0.05). Treatment with erythropoietin decreased the number of caspase 3 and TUNEL positive cells. The results of the study showed that erythropoietin administration is effective for recovery from degenerative changes in the ovary induced by the torsion-detorsion injury.

Intraoperative evaluation of testicular vascularization and perfusion in rat testicles with indocyanine green (ICG)/near-infrared (NIR) fluorescent imaging after torsion-detorsion and reperfusion.

The aim of this study was to evaluate testicular perfusion and vascularization with intraoperative ICG/NIR imaging in a testicular ischemia-reperfusion model and to investigate the effects of ICG on testicular tissue. 24 male rats were divided into four groups. In the ICG group, only ICG was given and images of the testicles were recorded with NIR camera. In the torsion group, the testicles were left in torsion for 4h. ICG/NIR images were obtained after torsion and detorsion. In the reperfusion group, ICG/NIR images of the testicles were obtained at the 4th hour of reperfusion. After the procedures, testicles were collected and evaluated with histological, immunohistochemical examination and qRT-PCR. There was no histologically negative effect of ICG on testicular tissue. There was no testicular perfusion in the torsion group, but perfusion started after detorsion. At the 4th hour of reperfusion, testicular perfusion continued. TNF-a, IL-6, MCP-1 and caspase-3 immunoreactivity were found to be at low levels in the control and ICG groups, while high in the torsion and reperfusion groups (p < 0.05). In qRT-PCR, TNF-a, IL-6, MCP-1 and caspase-3 expressions were lower in the control and ICG groups, but higher in the torsion and reperfusion groups. There was no histologically negative effect of ICG on testicles. The ICG/NIR imaging technique seems to be a feasible method in testicular torsion and may contribute to the surgeon in the intraoperative management of testicular torsion. In testicles that started to be perfused after detorsion, perfusion still continued at the 4th hour of reperfusion. Our next goal is to test whether testicles showing ICG fluorescence in during reperfusion maintain their viability for long term.

Automatic continuity for groups whose torsion subgroups are small

Abstract We prove that a group homomorphism φ : L → G \varphi\colon L\to G from a locally compact Hausdorff group 𝐿 into a discrete group 𝐺 either is continuous, or there exists a normal open subgroup N ⊆ L N\subseteq L such that φ ⁢ ( N ) \varphi(N) is a torsion group provided that 𝐺 does not include ℚ or the 𝑝-adic integers Z p \mathbb{Z}_{p} or the Prüfer 𝑝-group Z ⁢ ( p ∞ ) \mathbb{Z}(p^{\infty}) for any prime 𝑝 as a subgroup, and if the torsion subgroups of 𝐺 are small in the sense that any torsion subgroup of 𝐺 is artinian. In particular, if 𝜑 is surjective and 𝐺 additionally does not have non-trivial normal torsion subgroups, then 𝜑 is continuous. As an application, we obtain results concerning the continuity of group homomorphisms from locally compact Hausdorff groups to many groups from geometric group theory, in particular to automorphism groups of right-angled Artin groups and to Helly groups.

On the λ-stability of p-class groups along cyclic p-towers of a number field

Let [Formula: see text] be a number field, [Formula: see text] a prime and [Formula: see text] a set of finite places of [Formula: see text]. We call [Formula: see text] a totally [Formula: see text]-ramified cyclic [Formula: see text]-tower if [Formula: see text] and if [Formula: see text] is totally ramified. Using analogues of Chevalley’s formula [G. Gras, Invariant generalized ideal classes—Structure theorems for p-class groups in p-extensions, Proc. Math. Sci. 127(1) (2017) 1–34], we give an elementary proof of a stability theorem (Theorem 3.1) for generalized [Formula: see text]-class groups [Formula: see text] of the layers [Formula: see text]: let [Formula: see text] given in Definition 1.1 ([Formula: see text] for ordinary class groups); then [Formula: see text] for all [Formula: see text], if and only if [Formula: see text]. This improves the case [Formula: see text] of [T. Fukuda, Remarks on [Formula: see text]-extensions of number fields, Proc. Japan Acad. Ser. A 70(8) (1994) 264–266; J. Li, Y. Ouyang, Y. Xu and S. Zhang, l-Class groups of fields in Kummer towers, Publ. Mat. 66(1) (2022) 235–267; Y. Mizusawa, K. Yamamoto, On [Formula: see text]-class groups of relative cyclic [Formula: see text]-extensions, Arch. Math. 117(3) (2021) 253–260] whose techniques are based on Iwasawa’s theory or Galois theory of pro-[Formula: see text]-groups. We deduce promising capitulation properties of [Formula: see text] in the tower giving Conjecture 4.1. Finally, we apply our principles to the torsion groups [Formula: see text] of abelian [Formula: see text]-ramification theory. Numerical examples are given with PARI programs.

Regular languages for contracting geodesics

Let G $G$ be a finitely generated group. We show that for any finite symmetric generating set A $A$ , the language consisting of all geodesics in Cay ( G , A ) $(G,A)$ with the contracting property is a regular language. An immediate consequence is that the existence of an infinite contracting geodesic in a Cayley graph of a finitely generated group implies the existence of a contracting element. In particular, torsion groups cannot contain an infinite contracting geodesic. As an application, this implies that any finitely generated group containing an infinite contracting geodesic must be either virtually Z $\mathbb {Z}$ or acylindrically hyperbolic.

A retrospective cohort study on the clinical course of ovarian torsion in females with abdominal pain

Objective: The goal of this study was to examine the clinical and ultrasonographic features of females who presented with abdominal discomfort and had ovarian torsion against those who did not. Methods: This was a cohort study that looked back included all female patients who presented to a referral private clinic with pelvic and/or abdominal pain between January 2017 and December 2020. Patients who were clinically diagnosed with torsion but had negative intra-operative findings were excluded. Patients who met the criteria were separated into two groups (ovarian torsion vs. no torsion).Symptoms including the type, location and duration of pain, presence of nausea and vomiting, abdominal tenderness, presence of adnexal masses at digital examination, ultrasound findings, pre-operative diagnosis, final diagnosis, as well as surgical management were recorded. Results: During the research period, a total of 65 female patients came with abdominal discomfort, with 17 (26.2%) having ovarian torsion and 48 (73.8%) not having torsion. 1 (5.9%) of the 17 patients with torsion were in their teenage years, 14 (87.4%) were in their reproductive years, and 2 (11.8%) were 51 years or older. All patients who had torsion presented with nausea and vomiting while none of the patients who did not have torsion had nausea and vomiting (p-value&lt;0.0001). As for pain, 38 (79.2%) had moderate pain in the no torsion group compared to none in those who had torsion since all patients who had torsion had severe pain compared to 10 (20.8%) of those who did not have torsion (p-value&lt;0.0001). Eight patients were pregnant, 5 without torsion and 3 with torsion. The length of discomfort in the torsion group was substantially longer than in the non-torsion group (52.6555.02 days vs. 16.3115.85, p-value0.0001, respectively). Three patients were menopausal, 1 with no torsion and 2 had torsion. Around 58% of the patients without torsion had negative Doppler findings for simple cyst compared to 23.5% of those with torsion. All patients who had torsion underwent surgery and all patients without torsion had regression of pelvic mass. For those who had torsion, 35.3% had their ovary removed, 58.8% had the cyst removed while ovary conserved, and 5.9% had drainage for the cyst. Conclusion: Using a combination of presenting symptoms and ultrasonography, ovarian masses may be identified and ovarian torsion suspected. Torsion must be detected early in order to get conservative therapy and maintain the reproductive capacity of younger girls.

Torsion groups do not act on 2-dimensional CAT(0) complexes

We show, under mild hypotheses, that if each element of a finitely generated group acting on a 2-dimensional CAT(0) complex has a fixed point, then there is a global fixed point. In particular, all actions of finitely generated torsion groups on such complexes have global fixed points. The proofs rely on Masur’s theorem on periodic trajectories in rational billiards, and Ballmann–Brin’s methods for finding closed geodesics in 2-dimensional locally CAT(0) complexes. As another ingredient, we prove that the image of an immersed loop in a graph of girth 2π with length not commensurable with π has diameter >π. This is closely related to a theorem of Dehn on tiling rectangles by squares.

Protective effect of Smilax excelsa L. pretreatment via antioxidant, anti-inflammatory effects, and activation of Nrf-2/HO-1 pathway in testicular torsion model.

The protective effects of the ethanol extract of Smilax excelsa L. (SE) leaves were investigated on testicular tissue of rats with a torsion model in this study. The chemical composition of the extract was detected by means of liquid chromatography with tandem mass spectrometry (LC-MS/MS). SE extract was given for 21 days before torsion was created in the treatment group. The sperm parameters of the torsion group were impaired, and there was an increase in MDA level as well as a decrease in GSH level and GPx activity compared to the control group. TNF-α and NF-κB levels in the torsion group increased as compared to those in the control group. The expression levels of Nrf-2 and HO-1 were lower in the torsion group than those in the control group. The SE pretreatment group has improved sperm, oxidative stress, and inflammatory markers when compared to the torsion group, and the Nrf-2/HO-1 pathway was activated. PRACTICAL APPLICATIONS: Smilax excelsa L. is a plant with economic value used in traditional medicine in the treatment of stomachache, bloating, and breast cancer in Northwest Anatolia. It has an antioxidant effect due to the flavonoids and anthocyanins it contains. The protective effect against ischemia-reperfusion-induced tissue and reproductive damage in testicular tissue were demonstrated with the study. When the histological examinations of the tissues were evaluated, it was found that morphological structure of the tissues was retained in the treatment group. The findings indicate that SE prevents tissue damage in the torsion model by antioxidant and anti-inflammatory effects and activating Nrf-2/HO-1 pathway.

Counting elliptic curves with prescribed level structures over number fields

Harron and Snowden counted the number of elliptic curves over $\mathbb{Q}$ up to height $X$ with torsion group $G$ for each possible torsion group $G$ over $\mathbb{Q}$. In this paper we generalize their result to all number fields and all level structures $G$ such that the corresponding modular curve $X_G$ is a weighted projective line $\mathbb{P}(w_0,w_1)$ and the morphism $X_G\to X(1)$ satisfies a certain condition. In particular, this includes all modular curves $X_1(m,n)$ with coarse moduli space of genus $0$. We prove our results by defining a size function on $\mathbb{P}(w_0,w_1)$ following unpublished work of Deng, and working out how to count the number of points on $\mathbb{P}(w_0,w_1)$ up to size $X$.

Abelian networks IV. Dynamics of nonhalting networks

An abelian network is a collection of communicating automata whose state transitions and message passing each satisfy a local commutativity condition. This paper is a continuation of the abelian networks series of Bond and Levine (2016), for which we extend the theory of abelian networks that halt on all inputs to networks that can run forever. A nonhalting abelian network can be realized as a discrete dynamical system in many different ways, depending on the update order. We show that certain features of the dynamics, such as minimal period length, have intrinsic definitions that do not require specifying an update order. We give an intrinsic definition of the torsion group of a finite irreducible (halting or nonhalting) abelian network, and show that it coincides with the critical group of Bond and Levine (2016) if the network is halting. We show that the torsion group acts freely on the set of invertible recurrent components of the trajectory digraph, and identify when this action is transitive. This perspective leads to new results even in the classical case of sinkless rotor networks (deterministic analogues of random walks). In Holroyd et. al (2008) it was shown that the recurrent configurations of a sinkless rotor network with just one chip are precisely the unicycles (spanning subgraphs with a unique oriented cycle, with the chip on the cycle). We generalize this result to abelian mobile agent networks with any number of chips. We give formulas for generating series such as \[ ∑ n ≥ 1 r n z n = det ( 1 1 − z D − A ) \sum _{n \geq 1} r_n z^n = \det (\frac {1}{1-z}D - A ) \] where r n r_n is the number of recurrent chip-and-rotor configurations with n n chips; D D is the diagonal matrix of outdegrees, and A A is the adjacency matrix. A consequence is that the sequence ( r n ) n ≥ 1 (r_n)_{n \geq 1} completely determines the spectrum of the simple random walk on the network.

On Undecidability of Finite Subsets Theory for Torsion Abelian Groups

Let M be a commutative cancellative monoid with an element of infinite order. The binary operation can be extended to all finite subsets of M by the pointwise definition. So, we can consider the theory of finite subsets of M. Earlier, we have proved the following result: in the theory of finite subsets of M elementary arithmetic can be interpreted. In particular, this theory is undecidable. For example, the free monoid (the sets of all words with concatenation) has this property, the corresponding algebra of finite subsets is the theory of all finite languages with concatenation. Another example is an arbitrary Abelian group that is not a torsion group. But the method of proof significantly used an element of infinite order, hence, it can’t be immediately generalized to torsion groups. In this paper we prove the given theorem for Abelian torsion groups that have elements of unbounded order: for such group, the theory of finite subsets allows interpreting the elementary arithmetic.

On quartic Diophantine equations with trivial solutions in the Gaussian integers

We show that the quartic Diophantine equations $ax^4+by^4=cz^2$ has only trivial solution in the Gaussian integers for some particular choices of $a,b$ and $c$. Our strategy is by elliptic curves method. In fact, we exhibit two null-rank corresponding families of elliptic curves over Gaussian field. We also determine the torsion groups of both families.

G-Hypergroups: Hypergroups with a Group-Isomorphic Heart

Hypergroups can be subdivided into two large classes: those whose heart coincide with the entire hypergroup and those in which the heart is a proper sub-hypergroup. The latter class includes the family of 1-hypergroups, whose heart reduces to a singleton, and therefore is the trivial group. However, very little is known about hypergroups that are neither 1-hypergroups nor belong to the first class. The goal of this work is to take a first step in classifying G-hypergroups, that is, hypergroups whose heart is a nontrivial group. We introduce their main properties, with an emphasis on G-hypergroups whose the heart is a torsion group. We analyze the main properties of the stabilizers of group actions of the heart, which play an important role in the construction of multiplicative tables of G-hypergroups. Based on these results, we characterize the G-hypergroups that are of type U on the right or cogroups on the right. Finally, we present the hyperproduct tables of all G-hypergroups of size not larger than 5, apart of isomorphisms.

On elliptic curves induced by rational Diophantine quadruples

In this paper, we consider elliptic curves induced by rational Diophantine quadruples, i.e. sets of four non-zero rationals such that the product of any two of them plus 1 is a perfect square. We show that for each of the groups $\mathbf{Z}/2\mathbf{Z} \times \mathbf{Z}/k\mathbf{Z}$ for $k=2,4,6,8$, there are infinitely many rational Diophantine quadruples with the property that the induced elliptic curve has this torsion group. We also construct curves with moderately large rank in each of these four cases.