Minimal Subgroups Research Articles

Biomarkers of Neurobiologic Recovery in Adults With Sport-Related Concussion

ImportanceSport-related concussion (SRC), a form of mild traumatic brain injury, is a prevalent occurrence in collision sports. There are no well-established approaches for tracking neurobiologic recovery after SRC.ObjectiveTo examine the levels of serum glial fibrillary acidic protein (GFAP) and neurofilament light (NfL) in Australian football athletes who experience SRC.Design, Setting, and ParticipantsA cohort study recruiting from April 10, 2021, to September 17, 2022, was conducted through the Victorian Amateur Football Association, Melbourne, Australia. Participants included adult Australian football players with or without SRC. Data analysis was performed from May 26, 2023, to March 27, 2024.ExposureSport-related concussion, defined as at least 1 observable sign and/or 2 or more symptoms.Main Outcomes and MeasuresPrimary outcomes were serum GFAP and NfL levels at 24 hours, and 1, 2, 4, 6, 8, 12, and 26 weeks. Secondary outcomes were symptoms, cognitive performance, and return to training times.ResultsEighty-one individuals with SRC (median age, 22.8 [IQR, 21.3-26.0] years; 89% male) and 56 control individuals (median age, 24.6 [IQR, 22.4-27.3] years; 96% male) completed a total of 945 of 1057 eligible testing sessions. Compared with control participants, those with SRC exhibited higher GFAP levels at 24 hours (mean difference [MD] in natural log, pg/mL, 0.66 [95% CI, 0.50-0.82]) and 4 weeks (MD, 0.17 [95% CI, 0.02-0.32]), and NfL from 1 to 12 weeks (1-week MD, 0.31 [95% CI, 0.12-0.51]; 2-week MD, 0.38 [95% CI, 0.19-0.58]; 4-week MD, 0.31 [95% CI, 0.12-0.51]; 6-week MD, 0.27 [95% CI, 0.07-0.47]; 8-week MD, 0.36 [95% CI, 0.15-0.56]; and 12-week MD, 0.25 [95% CI, 0.04-0.46]). Growth mixture modeling identified 2 GFAP subgroups: extreme prolonged (16%) and moderate transient (84%). For NfL, 3 subgroups were identified: extreme prolonged (7%), moderate prolonged (15%), and minimal or no change (78%). Individuals with SRC who reported loss of consciousness (LOC) (33% of SRC cases) had higher GFAP at 24 hours (MD, 1.01 [95% CI, 0.77-1.24]), 1 week (MD, 0.27 [95% CI, 0.06-0.49]), 2 weeks (MD, 0.21 [95% CI, 0.004-0.42]) and 4 weeks (MD, 0.34 [95% CI, 0.13-0.55]), and higher NfL from 1 week to 12 weeks (1-week MD, 0.73 [95% CI, 0.42-1.03]; 2-week MD, 0.91 [95% CI, 0.61-1.21]; 4-week MD, 0.90 [95% CI, 0.59-1.20]; 6-week MD, 0.81 [95% CI, 0.50-1.13]; 8-week MD, 0.73 [95% CI, 0.42-1.04]; and 12-week MD, 0.54 [95% CI, 0.22-0.85]) compared with SRC participants without LOC. Return to training times were longer in the GFAP extreme compared with moderate subgroup (incident rate ratio [IRR], 1.99 [95% CI, 1.69-2.34]; NfL extreme (IRR, 3.24 [95% CI, 2.63-3.97]) and moderate (IRR, 1.43 [95% CI, 1.18-1.72]) subgroups compared with the minimal subgroup, and for individuals with LOC compared with those without LOC (IRR, 1.65 [95% CI, 1.41-1.93]).Conclusions and RelevanceIn this cohort study, a subset of SRC cases, particularly those with LOC, showed heightened and prolonged increases in GFAP and NfL levels, that persisted for at least 4 weeks. These findings suggest that serial biomarker measurement could identify such cases, guiding return to play decisions based on neurobiologic recovery. While further investigation is warranted, the association between prolonged biomarker elevations and LOC may support the use of more conservative return to play timelines for athletes with this clinical feature.

On finite groups in which all minimal subgroups are BNA-subgroups

A subgroup H of a group G is said to be a BNA-subgroup of G if either H^{x}= H or x \in \langle H, H^{x}\rangle for all x\in G . The purpose of this paper is first to give the best bound for the Fitting height of G if all minimal subgroups of G are BNA-subgroups of G , and next to give an answer to the question of He, Li, and Wang [Rend. Semin. Mat. Univ. Padova 136 (2016), 51–60]. Finally, we use a few BNA-subgroups of prime order to determine the structure of the finite groups. In fact, some new conditions for a finite group to be supersolvable have been given.

On splittings and integration of almost periodic functions with and without geometry

AbstractRecently, the authors introduced the notion of weighted semigroups which apply to sun-dual semigroups and especially to the translation semigroup on the space of left continuous functions with values in dual spaces. In this article, we will show that it is sufficient that we either assume geometry on the Banach, or an abelian structure on the minimal subgroup to prove almost periodicity. This yields a different approach to the almost periodicity of semigroups and integrals, by extending Basit generalized Kadets result to general groups, to obtain almost periodicity.

Finite Groups with Hereditarily $$G$$-Permutable Minimal Subgroups

Finite Groups with Hereditarily $$G$$-Permutable Minimal Subgroups

Finite groups with Hall normally embedded minimal subgroups

Let G be a finite group. A subgroup H of G is called Hall normally embedded in G if H is a Hall subgroup of H , where H is the normal closure of H in G, that is, the smallest normal subgroup of G containing H. A group G is called an HNE 2-group if all cyclic subgroups of order 2 and 4 of G are Hall normally embedded in G. In this paper, we prove that all HNE 2-groups are 2-nilpotent. Furthermore, we also characterize the structure of finite group all of whose maximal subgroups are HNE 2-groups. Finally, we determine finite non-solvable groups all of whose second maximal subgroups are HNE 2-groups.

Finite groups with minimal weakly BNA-subgroups

Let [Formula: see text] be a finite group. A subgroup [Formula: see text] of [Formula: see text] is said to be a BNA-subgroup of [Formula: see text] if either [Formula: see text] or [Formula: see text] for all [Formula: see text]. A subgroup [Formula: see text] of [Formula: see text] is said to be a weakly BNA-subgroup of [Formula: see text] if there exists a normal subgroup [Formula: see text] of [Formula: see text] such that [Formula: see text] and [Formula: see text] is a BNA-subgroup of [Formula: see text]. In this paper, we investigate the structure of a finite group [Formula: see text] under the assumption that every minimal subgroup of [Formula: see text] not having a supersolvable supplement in [Formula: see text] is a weakly BNA-subgroup of [Formula: see text].

On PN-groups and the norm of minimal subgroups

A finite group is called a [Formula: see text]-group if all its minimal subgroups are normal. In this paper, [Formula: see text]-groups were characterized by investigating on the generalized norm of minimal subgroups.

Intensive Outpatient Program Response Among Service Members With Mild Traumatic Brain Injury: Change Between Distinct Post-Concussive Symptom Subgroups

ObjectiveAmong service members (SMs) with mild traumatic brain injury (mTBI) admitted to an intensive outpatient program (IOP), we identified qualitatively distinct subgroups based on post-concussive symptoms (PCSs) and characterized changes between subgroups from admission to discharge. Further, we examined whether co-morbid posttraumatic stress disorder (PTSD) influenced changes between subgroups. DesignQuasi-experimental. Latent transition analysis identified distinctive subgroups of SMs and examined transitions between subgroups from admission to discharge. Logistic regression examined the effect of PTSD on transition to the Minimal subgroup (low probability of any moderate-very severe PCS) while adjusting for admission subgroup designation. SettingNational Intrepid Center of Excellence (NICoE) at Walter Reed National Military Medical Center. Participants1141 active duty SMs with persistent PCS despite prior treatment (N=1141). InterventionsNICoE 4-week interdisciplinary IOP. Main Outcome Measure(s)Subgroups identified using Neurobehavioral Symptom Inventory items at admission and discharge. ResultsModel fit indices supported a 7-class solution. The 7 subgroups of SMs were distinguished by diverging patterns of probability for specific PCS. The Minimal subgroup was most prevalent at discharge (39.4%), followed by the Sleep subgroup (high probability of sleep problems, low probability of other PCS; 26.8%). 41% and 25% of SMs admitted within the Affective (ie, predominantly affective PCS) and Sleep subgroups remained within the same group at discharge, respectively. The 19% of SMs with co-morbid PTSD were less likely to transition to the Minimal subgroup (odds ratio=0.28; P<.001) and were more likely to remain in their admission subgroup at discharge (35.5% with PTSD vs 22.2% without). ConclusionsMost of SMs achieved symptom resolution after participation in the IOP, with most transitioning to subgroups characterized by reduced symptom burden. SMs admitted in the Affective and Sleep subgroups, as well as those with PTSD, were most likely to have continuing clinical needs at discharge, revealing priority targets for resource allocation and follow-up treatment.

On Weakly ss-Supplemented Subgroups of Finite Groups

Let H be a subgroup of a finite group G. We say that H is weakly ss-supplemented in G if there exists a subgroup T of G and an s-semipermutable subgroup Hss of G contained in H such that G = HT and H∩T ≤ Hss. In this paper, we get some new characterizations of supersolvability and nilpotentcy of G by assuming some minimal subgroups of G are weakly ss-supplemented. Some recent results are extended and generalized.

The influence of supplemented subgroups on the structure of finite groups

A subgroup H of a finite group G is said to be supplemented in G if there exists a subnormal subgroup T of G such that G = HT and where is the Frattini subgroup of H. In this article, we investigate the structure of a finite group G under the assumption that certain subgroups of G are supplemented in G. We obtain that a finite group G is nilpotent if and only if every Sylow subgroup of G is supplemented in G. And a group G is nilpotent if every maximal subgroup of G is supplemented in G. Moreover, the commutativity of G is characterized by using that the minimal subgroups of two non–conjugate maximal subgroups of G are supplemented in G.

On weakly BNA-subgroups of finite groups

Let G be a finite group. A subgroup H of G is called a BNA-subgroup of G if either or for all A subgroup H of G is said to be a weakly BNA-subgroup of G if there exists a normal subgroup T of G such that G = HT and is a BNA-subgroup of G. In this paper, we investigate the solvability, supersolvability, and p-nilpotency of a finite group G under the assumption that certain minimal subgroups and cyclic subgroups of order 4 are weakly BNA-subgroups of G.

Finite groups with n-embedded subgroups

Let [Formula: see text] be a finite group. How minimal subgroups can be embedded in [Formula: see text] is a question of particular interest in studying the structure of [Formula: see text]. A subgroup [Formula: see text] of [Formula: see text] is called [Formula: see text]-permutable in [Formula: see text] if [Formula: see text] for all Sylow subgroups [Formula: see text] of [Formula: see text]. A subgroup [Formula: see text] of [Formula: see text] is called [Formula: see text]-embedded in [Formula: see text] if there exists a normal subgroup [Formula: see text] of [Formula: see text] such that [Formula: see text] and [Formula: see text], where [Formula: see text] is the subgroup of [Formula: see text] generated by all those subgroups of [Formula: see text] which are [Formula: see text]-permutable in [Formula: see text]. In this paper, we investigate the structure of the finite group [Formula: see text] with [Formula: see text]-embedded subgroups.

Finite groups with S-quasinormal subgroups

Let G be a finite group. A minimal subgroup of G is a subgroup of prime order. A subgroup of G is called S-quasinormal in G if it permutes with each Sylow subgroup of G. A group G is called an MS-group if each minimal subgroup of G is S-quasinormal in G. In this paper, we study the structure of finite groups all of whose maximal subgroups of even order are MS-groups. Furthermore, we determine the finite non-abelian simple groups all of whose second maximal subgroups of even order are MS-groups.

Max-min theorems for weak containment, square summable homoclinic points, and completely positive entropy

We prove a max-min theorem for weak containment the context of algebraic actions. Namely, we show that given an algebraic action of $G$ on $X,$ there is a maximal, closed $G$-invariant subgroup $Y$ of $X$ so that the action of $G$ on $Y$ is weakly contained a Bernoulli shift. This subgroup is also the minimal subgroup so that any action weakly contained a Bernoulli shift is $G\curvearrowright X/Y$-ergodic in the presence of $G\curvearrowright X$. We give several applications, including a major simplification of the proof that measure entropy equals topological entropy for principal algebraic actions whose associated convolution operator is injective. We also deduce from our techniques that algebraic actions whose square summable homoclinic group is dense have completely positive entropy when the acting group is sofic.

Obesity with radiological changes or depression was associated with worse knee outcome in general population: a cluster analysis in the Nagahama study

BackgroundIn knee osteoarthritis (OA), pain is the most frequent and dominant symptom. However, which factors other than radiological changes contribute to the symptoms is unresolved. The aims of this study were to identify factors affecting knee pain from various variables with radiological changes taken into count and exploratively examine what subgroups or phenotype could be identified by cluster analysis using the identified knee pain factors.MethodsPatients 60 years or older who underwent radiographic evaluation were included in this cross-sectional study, and those subjects who completed a questionnaire about knee symptoms without missing data were eligible for analysis. Multiple regression analysis was used to examine the associations between selected variables and The Japanese Knee Osteoarthritis Measure (JKOM) pain score. We grouped the subjects by cluster analysis using identified variables.ResultsTwo thousand five hundred forty-two subjects were included in the full set of analyses. Age, body mass index (BMI), radiological grade, bone mineral density (BMD), and high-sensitivity C-reactive protein (hs-CRP) showed a statistically significant correlation with radiological showing the strongest value. For dichotomous variable, presence of depression showed a statistically significant result. We used BMI, radiological grade, BMD, hs-CRP, and presence of depression as a variable for cluster analysis and identified six subgroups: (1) minimal joint disease subgroup, (2) male and high BMD subgroup, (3) high CRP subgroup, (4) severe radiological OA subgroup, (5) depressive subgroup, and (6) moderate radiological OA with high BMI subgroup, showing the worst knee outcome.ConclusionThis study identified the factors affecting knee pain other than radiological changes and identified six subgroups of knee outcome in the general population. The results showed that obesity with radiological changes or depression was associated with worse knee outcome.

Topological Conjugation Classes of Tightly Transitive Subgroups of $$\text {Homeo}_{+}(\mathbb {S}^1)$$

Let \(\text {Homeo}_{+}(\mathbb {S}^1)\) denote the group of orientation preserving homeomorphisms of the circle \(\mathbb {S}^1\). A subgroup G of \(\text {Homeo}_{+}(\mathbb {S}^1)\) is tightly transitive if it is topologically transitive and no subgroup H of G with \([G: H]=\infty \) has this property; is almost minimal if it has at most countably many nontransitive points. In the paper, we determine all the topological conjugation classes of tightly transitive and almost minimal subgroups of \(\text {Homeo}_{+}(\mathbb {S}^1)\) which are isomorphic to \(\mathbb {Z}^n\) for any integer \(n\ge 2\).

Cardinal invariants and convergence properties of locally minimal groups

Let G be a locally essential subgroup of a locally compact abelian group K. Then:(i)t(G)=χ(G)=χ(K), where t(G) and χ(G) are the tightness and the character of G, respectively;(ii)if G is radial, then K must be metrizable;(iii)if G is non-discrete, then G contains a super-sequence S converging to 0 such that |S|=χ(G)=χ(K); in particular, G has non-trivial convergent sequences.Items (i)–(iii) hold when G is a dense locally minimal subgroup of K. It follows that locally minimal, locally precompact abelian groups of countable tightness are metrizable. In particular, a minimal abelian group of countable tightness is metrizable. This answers a question of O. Okunev posed in 2007.For every uncountable cardinal κ, we construct a Fréchet-Urysohn minimal nilpotent group G of nilpotency class 2 and character κ such that the connected component of G is an open normal ω-bounded subgroup of G (thus, G is locally precompact). We also build a minimal nilpotent group of nilpotency class 2 without non-trivial convergent sequences having an open normal countably compact subgroup.

On Finite Groups with Some Minimal Subgroups Weakly Supplemented

A subgroup H of a finite group G is weakly supplemented in G if there exists a proper subgroup K of G such that $$G=HK$$. In the paper, we present some sufficient and necessary conditions for a finite group to be p-nilpotent and solvable by using some weakly supplemented minimal subgroups. As applications, we extend some known results.

Finite groups with some minimal subgroups are ℋC-subgroups

A subgroup [Formula: see text] of a group [Formula: see text] is said to be an [Formula: see text]-subgroup of [Formula: see text], if there exists a normal subgroup [Formula: see text] of [Formula: see text] such that [Formula: see text] and [Formula: see text], for all [Formula: see text]. In this paper, we investigate the structure of groups based on the assumption that every subgroup of [Formula: see text] of order [Formula: see text] or 4 (if [Formula: see text]) is an [Formula: see text]-subgroup of [Formula: see text], here [Formula: see text] is a Sylow [Formula: see text]-subgroup of [Formula: see text]. Some results for a group to be [Formula: see text]-nilpotent and supersolvable are obtained and many known results are generalized.

English

A subgroup H of a finite group G is weakly-supplemented in G if there exists a proper subgroup K of G such that G = HK. In this paper, some interesting results with weakly-supplemented minimal subgroups to a smaller subgroup of G are obtained.