Results 21 to 30 of about 228,002 (82)

A Frobenius-type theorem for supersolvable groups

Publicationes mathematicae (Debrecen), 1996
Frobenius’ Theorem for p-nilpotent groups is one of the most fundamental theorems in finite group theory. In this paper a Frobenius-type Theorem for supersolvable groups is given by applying strictly p-closed groups, and some applications are obtained ...
Wang Caiyun, Guo Xiuyun
semanticscholar   +1 more source

A note on influence of subgroup restrictions in finite group structure

International Journal of Mathematics and Mathematical Sciences, Volume 12, Issue 4, Page 721-724, 1989., 1988
The structure of a finite group under specific restrictions respectively on its maximal, minimal and prime power subgroups has been investigated in this paper.
R. Khazal, N. P. Mukherjee
wiley   +1 more source

$G$-permutable Subgroups in $\operatorname{PSL}_2(q)$ and Hereditarily $G$-permutable Subgroups in $\operatorname{PSU}_3(q)$

Известия Иркутского государственного университета: Серия "Математика"
The concept of $X$-permutable subgroup, introduced by A. N. Skiba, generalizes the classical concept of a permutable subgroup. Many classes of finite groups have been characterized in terms of $X$-permutable subgroups.
A. A. Galt, V. N. Tyutyanov
doaj   +1 more source

A Jordan–Chevalley decomposition beyond algebraic groups

Journal of the London Mathematical Society, Volume 111, Issue 6, June 2025.
Abstract We prove a decomposition of definable groups in o‐minimal structures generalizing the Jordan–Chevalley decomposition of linear algebraic groups. It follows that any definable linear group G$G$ is a semidirect product of its maximal normal definable torsion‐free subgroup N(G)$\mathcal {N}(G)$ and a definable subgroup P$P$, unique up to ...
Annalisa Conversano
wiley   +1 more source

Sufficient conditions for the solvability and supersolvability in finite groups

Journal of Pure and Applied Algebra, 1984
A finite group G is called an H-r N-group if i) G has even order and ii) each even-ordered subgroup H of G with \(| H|\) the product of r not necessarily distinct primes, is normal in G. The author proves the following results: 1. If G is an H-2 N-group that does not involve \(A_ 4\), then G is supersolvable. 2. If G is an H-2 N-group or an H-3 N-group
openaire   +1 more source

On finite d$d$‐maximal groups

Bulletin of the London Mathematical Society, Volume 56, Issue 3, Page 1054-1070, March 2024.
Abstract Let d$d$ be a positive integer. A finite group is called d$d$‐maximal if it can be generated by precisely d$d$ elements, whereas its proper subgroups have smaller generating sets. For d∈{1,2}$d\in \lbrace 1,2\rbrace$, the d$d$‐maximal groups have been classified up to isomorphism and only partial results have been proved for larger d$d$.
Andrea Lucchini, Luca Sabatini, Mima Stanojkovski   +2 more
wiley   +1 more source

A new kind of polynomials for finite groups

Ricerche di Matematica
Let Property X be a certain property of some finite groups; for instance, nilpotent, supersolvable, solvable et cetera. The Thompson-like problem asks whether for two finite groups G1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym}
A. K. Asboei, C. Anabanti
semanticscholar   +1 more source

Isomorphic subgroups of solvable groups

, 2015
I. Isaacs, G. Robinson
semanticscholar   +1 more source

A NOTE ON PRIMITIVE SUBGROUPS OF FINITE SOLVABLE GROUPS

, 2013
Xuanli He, S. Qiao, Yanming Wang
semanticscholar   +1 more source

Counting supersolvable and solvable group orders

Research in Mathematics
Edward Bertram, Guanhong Li
openaire   +1 more source