Results 31 to 40 of about 581,922 (233)

On soluble groups whose subnormal subgroups are inert [PDF]

International Journal of Group Theory, 2015
A subgroup H of a group G is called inert if‎, ‎for each g∈G ‎, ‎the index of H∩H g in H is finite‎. ‎We give a classification ‎of soluble-by-finite groups G in which subnormal subgroups are inert in the cases where G has no nontrivial torsion ...
Ulderico Dardano , Silvana Rinauro
doaj  

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, A. Ballester-Bolinches, Mohammed Al-Shomrani, R. A. Al-Obidy   +3 more
doaj   +1 more source

Locally finite p-groups with all subgroups either subnormal or nilpotent-by-Chernikov [PDF]

International Journal of Group Theory, 2012
We pursue further our investigation, begun in [H.~Smith, Groups with all subgroups subnormal or nilpotent-by-{C}hernikov, emph{Rend. Sem. Mat. Univ. Padova} 126 (2011), 245--253] and continued in [G.~Cutolo and H.~Smith, Locally finite groups with all ...
H. Smith, G. Cutolo
doaj  

On weakly $N$-subnormal subgroups of finite groups

Rendiconti del Seminario Matematico della Universita di Padova
Let G be a finite group and A, N\leq G .
A-Ming Liu, Muzhi Wang, Vasilly G. Safonov, A. N. Skiba   +3 more
semanticscholar   +1 more source

On $\sigma$-$c$-subnormal subgroups of finite groups

Hacettepe Journal of Mathematics and Statistics
Let $ \sigma=\{\sigma_i:i\in I\} $ be a partition of the set $ \mathbb{P} $ of all primes. A finite group $ G $ is called $ \sigma $-primary if the prime divisors, if any, of $|G|$ all belong to the same member of $ \sigma $.
Jiahui Li̇u, Sh. Qiao
semanticscholar   +1 more source

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

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, Ballester-Bolinches, Adolfo   +1 more
core   +1 more source

On the residual and profinite closures of commensurated subgroups

, 2019
The residual closure of a subgroup $H$ of a group $G$ is the intersection of all virtually normal subgroups of $G$ containing $H$. We show that if $G$ is generated by finitely many cosets of $H$ and if $H$ is commensurated, then the residual closure of ...
Caprace, Pierre-Emmanuel, Kropholler, Peter H., Reid, Colin D., Wesolek, Phillip   +3 more
core   +1 more source

On numbers which are orders of nilpotent groups with bounded class [PDF]

International Journal of Group Theory
Let $n$ be a positive integer. In this short note, we characterize those numbers $m$ for which any group of order $m$ is an $n$-Engel group and those numbers $m$ for which any group of order $m$ has all its subgroups subnormal of defect at most $n$.
Maria Ferrara
doaj   +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