Results 31 to 40 of about 682,067 (218)
Frattini Argument for Hall subgroups
, 2014 In the paper, it is proved that if a finite group $G$ possesses a $\pi$-Hall subgroup for a set $\pi$ of primes, then every normal subgroup $A$ of $G$ possesses a $\pi$-Hall subgroup $H$ such that ${G=AN_G(H)}$
Revin, Danila, Vdovin, Evgeny
core +1 more source
The Hochschild-Serre property for some p-adic analytic group actions
, 2015 Let $H \subseteq G$ be an inclusion of $p$-adic Lie groups. When $H$ is normal or even subnormal in $G$, the Hochschild-Serre spectral sequence implies that any continuous $G$-module whose $H$-cohomology vanishes in all degrees also has vanishing $G ...
Kedlaya, Kiran S.
core +1 more source
On σ-Residuals of Subgroups of Finite Soluble Groups
Mathematics, 2023 Let σ={σi:i∈I} be a partition of the set of all prime numbers. A subgroup H of a finite group G is said to be σ-subnormal in G if H can be joined to G by a chain of subgroups H=H0⊆H1⊆⋯⊆Hn=G where, for every j=1,⋯,n, Hj−1 is normal in Hj or Hj/CoreHj(Hj−1)
A. A. Heliel +3 more
doaj +1 more source
On the Frattini subgroup of a finite group
, 2016 We study the class of finite groups $G$ satisfying $\Phi (G/N)= \Phi(G)N/N$ for all normal subgroups $N$ of $G$. As a consequence of our main results we extend and amplify a theorem of Doerk concerning this class from the soluble universe to all finite ...
Aivazidis, Stefanos +1 more
core +1 more source
A Survey of Subnormal Subgroups
Irish Mathematical Society Bulletin, 1990 The author gives a survey (without proofs) of the high points of the theory of subnormal subgroups developed over the last fifty years. The article is intended as an introduction to the book by Lennox and Stonehewer.
openaire +2 more sources
Weakly subnormal subgroups and variations of the Baer–Suzuki theorem [PDF]
Journal of the London Mathematical SocietyA subgroup R$R$ of a finite group G$G$ is weakly subnormal in G$G$ if R$R$ is not subnormal in G$G$ but it is subnormal in every proper overgroup of R$R$ in G$G$ . In this paper, we first classify all finite groups G$G$ that contains a weakly subnormal p$
R. Guralnick, H. Tong‐Viet, G. Tracey
semanticscholar +1 more source
Groups with conjugacy classes of coprime sizes
Bulletin of the London Mathematical Society, Volume 58, Issue 3, March 2026.Abstract Suppose that x$x$, y$y$ are elements of a finite group G$G$ lying in conjugacy classes of coprime sizes. We prove that ⟨xG⟩∩⟨yG⟩$\langle x^G \rangle \cap \langle y^G \rangle$ is an abelian normal subgroup of G$G$ and, as a consequence, that if x$x$ and y$y$ are π$\pi$‐regular elements for some set of primes π$\pi$, then xGyG$x^G y^G$ is a π ...
R. D. Camina +8 more
wiley +1 more source
Joins of $\sigma$-subnormal subgroups
, 2023 Let $\sigma=\{\sigma_j\,:\, j\in J\}$ be a partition of the set $\mathbb{P}$ of all prime numbers. A subgroup $X$ of a finite group $G$ is~\textit{$\sigma$-subnormal} in $G$ if there exists a chain of subgroups $$X=X_0\leq X_1\leq\ldots\leq X_n=G$$ such that, for each $1\leq i\leq n-1$, $X_{i-1}\trianglelefteq X_i$ or $X_i/(X_{i-1})_{X_i}$ is a ...
Ferrara, Maria, Trombetti, Marco
openaire +2 more sources
On the join of subnormal subgroups [PDF]
Proceedings of the American Mathematical Society, 1974 Let G \mathfrak {G} be the class of finitely generated groups. If the join of finitely many subnormal X = s n X \mathfrak {X} = sn\mathfrak {X} subgroups is always an X \mathfrak {X} -group and
openaire +1 more source
Acta Ophthalmologica, Volume 104, Issue 1, Page 65-74, February 2026.Abstract Purpose The Extremely Preterm Infants in Sweden Study (EXPRESS) followed a national cohort of extremely preterm born (EPT, i.e. <27 weeks) children until 12 years of age. This study aimed to investigate the longitudinal development of visual acuity (VA) in children born EPT, explore the predictive value of early visual assessments, and ...
Despoina Tsamadou +12 more
wiley +1 more source