Results 161 to 170 of about 682,067 (218)

Finite groups with K--subnormal Schmidt subgroups

, 2021
Throughout this article, all groups are finite. Let be a formation of groups. A subgroup A of a finite group G is said to be K- -subnormal in G if there is a subgroup chain such that either or for all .
B. Hu, Jianhong Huang, D. Song, I. N. Safonova   +3 more
semanticscholar   +1 more source

NILPOTENT SUBGROUPS OF GROUPS WITH ALL SUBGROUPS SUBNORMAL

Bulletin of the London Mathematical Society, 2003
The main result of this remarkable paper is the following theorem: If \(G\) is a group with all subgroups subnormal and \(S\) is a nilpotent subgroup, then the normal closure \(S^G\) is also nilpotent. It follows from here that a group with all subgroups subnormal is a Fitting group (i.e.
openaire   +2 more sources

Maximal Subgroups of Almost Subnormal Subgroups in Division Rings

Acta Mathematica Vietnamica, 2021
A subgroup \(H\) of \(G\) is called ``almost subnormal'' if there exists a finite sequence of subgroups \(H=H_1 < H_2 < \dots
openaire   +1 more source

On weakly subnormal subgroups which are not subnormal

Archiv der Mathematik, 1987
A subgroup H of a group G is said to be n-step weakly subnormal in G (written \(H\leq ^ nG)\), for some integer \(n\geq 0\), if there are subsets \(S_ i\) of G such that \(H=S_ 0\subseteq S_ 1\subseteq...\subseteq S_ n=G\) with \(u^{-1}Hu\subseteq S_ i\) for all \(u\in S_{i+1}\), \(0\leq i\leq n-1\). Subnormal subgroups are clearly weakly subnormal and
Maruo, O., Stonehewer, S. E.
openaire   +2 more sources

Subnormality in the join of two subgroups

Journal of Group Theory, 2004
Let \(G=\langle U,V\rangle\) be a group generated by two subgroups \(U\) and \(V\), and let \(H\) be a subgroup of \(U\cap V\) which is subnormal in both \(U\) and \(V\). It is well known that \(H\) need not be subnormal in \(G\), even in the case of finite groups.
CASOLO, CARLO, U. Dardano
openaire   +3 more sources

Finite groups in which some particular invariant subgroups are TI-subgroups or subnormal subgroups

Georgian Mathematical Journal
Let A and G be finite groups such that A acts coprimely on G by automorphisms. We prove that if every self-centralizing non-nilpotent A-invariant subgroup of G is a TI-subgroup or a subnormal subgroup, then every non-nilpotent A-invariant subgroup of G ...
Yifan Liu, Jiangtao Shi
semanticscholar   +1 more source

Groups with subnormal or modular Schmidt 𝑝𝑑-subgroups

Journal of group theroy
A Schmidt group is a finite non-nilpotent group such that every proper subgroup is nilpotent. In this paper, we prove that if every Schmidt subgroup of a finite group 𝐺 is subnormal or modular, then G / F ⁢ ( G ) G/F(G) is cyclic.
V. Monakhov, I. Sokhor
semanticscholar   +1 more source

Finite groups with subnormal Schmidt subgroups

Algebra and Logic, 2007
Summary: We give a complete description of the structure of finite non-nilpotent groups all Schmidt subgroups of which are subnormal.
openaire   +1 more source

Hypercentral Groups with all Subgroups Subnormal II

Bulletin of the London Mathematical Society, 1986
It is shown that a hypercentral group that has all subgroups subnormal and every non-nilpotent subgroup of bounded defect is nilpotent. As a consequence, a hypercentral group of length at most ω in which every subgroup is subnormal is nilpotent.
openaire   +3 more sources

A note on self-centralizing subgroups and general subgroups of finite groups being a TI-subgroup or subnormal

Journal of Algebra and its Applications, 2022
Jiangtao Shi
semanticscholar   +1 more source