scholarly journals The maximal subgroups of Sylow subgroups and the structure of finite groups

2017 ◽  
Vol 37 (1) ◽  
pp. 113-124
Author(s):  
Changwen Li ◽  
Xuemei Zhang ◽  
Jianhong Huang
Keyword(s):  
Finite Groups ◽  
Maximal Subgroups ◽  
Sylow Subgroups

In this paper we investigate the influence of some subgroups of Sylow subgroups with semi cover-avoiding property and $E$-supplementation on the structure of finite groups. Some recent results are generalized and unified.

Finite groups with two supersoluble subgroups

2019 ◽  
Vol 22 (2) ◽  
pp. 297-312 ◽  
Author(s):  
Victor S. Monakhov ◽  
Alexander A. Trofimuk
Keyword(s):  
Finite Group ◽  
Finite Groups ◽  
Sufficient Conditions ◽  
Maximal Subgroups ◽  
Sylow Subgroups ◽  
Derived Subgroup ◽  
Nilpotent Residual ◽  
A Finite Group

AbstractLetGbe a finite group. In this paper we obtain some sufficient conditions for the supersolubility ofGwith two supersoluble non-conjugate subgroupsHandKof prime index, not necessarily distinct. It is established that the supersoluble residual of such a group coincides with the nilpotent residual of the derived subgroup. We prove thatGis supersoluble in the following cases: one of the subgroupsHorKis nilpotent; the derived subgroup{G^{\prime}}ofGis nilpotent;{|G:H|=q>r=|G:K|}andHis normal inG. Also the supersolubility ofGwith two non-conjugate maximal subgroupsMandVis obtained in the following cases: all Sylow subgroups ofMand ofVare seminormal inG; all maximal subgroups ofMand ofVare seminormal inG.

On Semi Cover-Avoiding Maximal Subgroups of Sylow Subgroups of Finite Groups

2009 ◽  
Vol 37 (4) ◽  
pp. 1160-1169 ◽  
Author(s):  
Yangming Li ◽  
Long Miao ◽  
Yanming Wang
Keyword(s):  
Finite Groups ◽  
Maximal Subgroups ◽  
Sylow Subgroups

On ℳ-Permutable Maximal Subgroups of Sylow Subgroups of Finite Groups

2010 ◽  
Vol 38 (10) ◽  
pp. 3649-3659
Author(s):  
Long Miao ◽  
Wolfgang Lempken
Keyword(s):  
Finite Groups ◽  
Maximal Subgroups ◽  
Sylow Subgroups

X-permutable maximal subgroups of Sylow subgroups of finite groups

2006 ◽  
Vol 58 (10) ◽  
pp. 1471-1480 ◽  
Author(s):  
W. Guo ◽  
K. P. Shum ◽  
A. N. Skiba
Keyword(s):  
Finite Groups ◽  
Maximal Subgroups ◽  
Sylow Subgroups

Groups with maximal subgroups of Sylow subgroups σ-permutably embedded

2017 ◽  
Vol 20 (1) ◽  
Author(s):  
Wenbin Guo ◽  
Alexander N. Skiba
Keyword(s):  
Finite Groups ◽  
Maximal Subgroups ◽  
Sylow Subgroups

AbstractLetIn this paper, we classify the finite groups

scholarly journals Maximal subgroups and PST-groups

2013 ◽  
Vol 11 (6) ◽  
Author(s):  
Adolfo Ballester-Bolinches ◽  
James Beidleman ◽  
Ramón Esteban-Romero ◽  
Vicent Pérez-Calabuig
Keyword(s):  
Finite Groups ◽  
Maximal Subgroups ◽  
Transitive Relation ◽  
Supersolvable Groups ◽  
Sylow Subgroups ◽  
Or Groups

AbstractA subgroup H of a group G is said to permute with a subgroup K of G if HK is a subgroup of G. H is said to be permutable (resp. S-permutable) if it permutes with all the subgroups (resp. Sylow subgroups) of G. Finite groups in which permutability (resp. S-permutability) is a transitive relation are called PT-groups (resp. PST-groups). PT-, PST- and T-groups, or groups in which normality is transitive, have been extensively studied and characterised. Kaplan [Kaplan G., On T-groups, supersolvable groups, and maximal subgroups, Arch. Math. (Basel), 2011, 96(1), 19–25] presented some new characterisations of soluble T-groups. The main goal of this paper is to establish PT- and PST-versions of Kaplan’s results, which enables a better understanding of the relationships between these classes.

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