The Influence of Minimal Subgroups on the Structure of Finite Groups

2000 ◽  
Vol 16 (1) ◽  
pp. 63-70 ◽  
Author(s):  
Yanming Wang
Keyword(s):  
Finite Groups ◽  
Minimal Subgroups

Finite Groups Whose Minimal Subgroups are Weakly -SUBGROUPS

2012 ◽  
Vol 32 (6) ◽  
pp. 2295-2301 ◽  
Author(s):  
M.M. Al-Mosa Al-Shomrani ◽  
M. Ramadan ◽  
A.A. Heliel
Keyword(s):  
Finite Groups ◽  
Minimal Subgroups

On weakly SS-quasinormal minimal subgroups of finite groups

2011 ◽  
Vol 78 (1) ◽  
pp. 209-218
Author(s):  
XIANGGUI ZHONG ◽  
SHIRONG LI
Keyword(s):  
Finite Groups ◽  
Minimal Subgroups

Finite groups with some minimal subgroups are ℋC-subgroups

2019 ◽  
Vol 18 (05) ◽  
pp. 1750062
Author(s):  
Xianbiao Wei
Keyword(s):  
Normal Subgroup ◽  
Finite Groups ◽  
Minimal 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.

Weakly s-supplementally embedded minimal subgroups of finite groups

2011 ◽  
Vol 54 (3) ◽  
pp. 799-807 ◽  
Author(s):  
Tao Zhao ◽  
Xianhua Li ◽  
Yong Xu
Keyword(s):  
Finite Group ◽  
Finite Groups ◽  
Minimal Subgroups ◽  
A Finite Group

AbstractSuppose that G is a finite group and H is a subgroup of G. We call H a weakly s-supplementally embedded subgroup of G if there exist a subgroup T of G and an s-quasinormally embedded subgroup Hse of G contained in H such that G = HT and H ∩ T ≤ Hse. We investigate the influence of the weakly s-supplementally embedded property of some minimal subgroups on the structure of finite groups. As an application of our results, some earlier results are generalized.

Finite groups with S-permutable n-minimal subgroups

2018 ◽  
Vol 46 (7) ◽  
pp. 3198-3204 ◽  
Author(s):  
Hongfei Pan ◽  
Guohua Qian
Keyword(s):  
Finite Groups ◽  
Minimal Subgroups

scholarly journals THE $c$-SUPPLEMENTED PROPERTY OF FINITE GROUPS

2007 ◽  
Vol 50 (2) ◽  
pp. 493-508 ◽  
Author(s):  
Huaquan Wei ◽  
Yanming Wang
Keyword(s):  
Finite Groups ◽  
Minimal Subgroups

AbstractThe purpose of this paper is to study the influence of $c$-supplemented minimal subgroups on the $p$-nilpotency of finite groups. We obtain ‘iff' and ‘localized' versions of theorems of Itô and Buckley on nilpotence, $p$-nilpotence and supersolvability.

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