On mutually permutable products of finite groups

2012 ◽  
Vol 139 (4) ◽  
pp. 344-353
Author(s):  
A. A. Heliel ◽  
Rola A. Hijazi
Keyword(s):  
Finite Groups ◽  
Mutually Permutable Products

scholarly journals Mutually Permutable Products of Finite Groups

ISRN Algebra ◽  
2011 ◽  
Vol 2011 ◽  
pp. 1-4
Author(s):  
Rola A. Hijazi
Keyword(s):  
Finite Group ◽  
Finite Groups ◽  
Sylow Subgroups ◽  
A Finite Group ◽  
Mutually Permutable Products

Let G be a finite group and G1, G2 are two subgroups of G. We say that G1 and G2 are mutually permutable if G1 is permutable with every subgroup of G2 and G2 is permutable with every subgroup of G1. We prove that if is the product of three supersolvable subgroups G1, G2, and G3, where Gi and Gj are mutually permutable for all i and j with and the Sylow subgroups of G are abelian, then G is supersolvable. As a corollary of this result, we also prove that if G possesses three supersolvable subgroups whose indices are pairwise relatively prime, and Gi and Gj are mutually permutable for all i and j with , then G is supersolvable.

On mutually permutable products of generalized supersoluble subgroups of finite groups

2016 ◽  
Vol 09 (03) ◽  
pp. 1650054
Author(s):  
E. N. Myslovets
Keyword(s):  
Finite Group ◽  
Simple Group ◽  
Finite Groups ◽  
Simple Groups ◽  
Finite Simple Groups ◽  
Paper Properties ◽  
Supersoluble Groups ◽  
A Finite Group ◽  
Mutually Permutable Products ◽  
Composition Factors

Let [Formula: see text] be a class of finite simple groups. We say that a finite group [Formula: see text] is a [Formula: see text]-group if all composition factors of [Formula: see text] are contained in [Formula: see text]. A group [Formula: see text] is called [Formula: see text]-supersoluble if every chief [Formula: see text]-factor of [Formula: see text] is a simple group. In this paper, properties of mutually permutable products of [Formula: see text]-supersoluble finite groups are studied. Some earlier results on mutually permutable products of [Formula: see text]-supersoluble groups (SC-groups) appear as particular cases.

scholarly journals Mutually Permutable Products of Finite Groups, II

1999 ◽  
Vol 218 (2) ◽  
pp. 563-572 ◽  
Author(s):  
A. Ballester-Bolinches ◽  
M.C. Pedraza-Aguilera
Keyword(s):  
Finite Groups ◽  
Mutually Permutable Products

scholarly journals Some classes of finite groups and mutually permutable products

2008 ◽  
Vol 319 (8) ◽  
pp. 3343-3351 ◽  
Author(s):  
M. Asaad ◽  
A. Ballester-Bolinches ◽  
J.C. Beidleman ◽  
R. Esteban-Romero
Keyword(s):  
Finite Groups ◽  
Mutually Permutable Products

scholarly journals On mutually permutable products of finite groups

2018 ◽  
Vol 29 (4) ◽  
pp. 711-719
Author(s):  
Adolfo Ballester-Bolinches ◽  
Yangming Li ◽  
Mari Carmen Pedraza-Aguilera ◽  
Ning Su
Keyword(s):  
Finite Groups ◽  
Mutually Permutable Products

scholarly journals On mutually permutable products of finite groups

2005 ◽  
Vol 294 (1) ◽  
pp. 127-135 ◽  
Author(s):  
A. Ballester-Bolinches ◽  
John Cossey ◽  
M.C. Pedraza-Aguilera
Keyword(s):  
Finite Groups ◽  
Mutually Permutable Products

Totally and mutually permutable products of finite groups

2013 ◽  
pp. 65-68 ◽  
Author(s):  
A Ballester-Bolinches ◽  
M D Pérez-Ramos ◽  
M C Pedraza-Aguilera
Keyword(s):  
Finite Groups ◽  
Mutually Permutable Products

scholarly journals Mutually Permutable Products of Finite Groups

1999 ◽  
Vol 213 (1) ◽  
pp. 369-377 ◽  
Author(s):  
A. Ballester-Bolinches ◽  
M.D. Pérez-Ramos ◽  
M.C. Pedraza-Aguilera
Keyword(s):  
Finite Groups ◽  
Mutually Permutable Products
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