scholarly journals ON GENERALISED FC-GROUPS IN WHICH NORMALITY IS A TRANSITIVE RELATION

2015 ◽  
Vol 100 (2) ◽  
pp. 192-198
Author(s):  
R. ESTEBAN-ROMERO ◽  
G. VINCENZI
Keyword(s):  
Conjugacy Classes ◽  
Maximal Subgroups ◽  
Transitive Relation ◽  
Supersolvable Groups

We extend to soluble $\text{FC}^{\ast }$-groups, the class of generalised FC-groups introduced in de Giovanni et al. [‘Groups with restricted conjugacy classes’, Serdica Math. J. 28(3) (2002), 241–254], the characterisation of finite soluble T-groups obtained recently in Kaplan [‘On T-groups, supersolvable groups, and maximal subgroups’, Arch. Math. (Basel) 96(1) (2011), 19–25].

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.

Maximal subgroups of GL n (D) with finite conjugacy classes

2009 ◽  
Vol 130 (3) ◽  
pp. 287-293 ◽  
Author(s):  
Dariush Kiani ◽  
Mojtaba Ramezan-Nassab
Keyword(s):  
Conjugacy Classes ◽  
Maximal Subgroups ◽  
Finite Conjugacy

scholarly journals Designs from maximal subgroups and conjugacy classes of Ree groups

2020 ◽  
Vol 14 (4) ◽  
pp. 603-611
Author(s):  
Jamshid Moori ◽  
◽  
Bernardo G. Rodrigues ◽  
Amin Saeidi ◽  
Seiran Zandi ◽  
...  
Keyword(s):  
Conjugacy Classes ◽  
Maximal Subgroups

Some sufficient conditions on solvability of finite groups

2016 ◽  
Vol 15 (03) ◽  
pp. 1650057 ◽  
Author(s):  
Wei Meng ◽  
Jiakuan Lu ◽  
Li Ma ◽  
Wanqing Ma
Keyword(s):  
Finite Group ◽  
Finite Groups ◽  
Sufficient Conditions ◽  
Conjugacy Classes ◽  
Maximal Subgroups ◽  
Prime Divisors ◽  
Abelian Subgroups ◽  
A Finite Group

For a finite group [Formula: see text], the symbol [Formula: see text] denotes the set of the prime divisors of [Formula: see text] denotes the number of conjugacy classes of maximal subgroups of [Formula: see text]. Let [Formula: see text] denote the number of conjugacy classes of non-abelian subgroups of [Formula: see text] and [Formula: see text] denote the number of conjugacy classes of all non-normal non-abelian subgroups of [Formula: see text]. In this paper, we consider the finite groups with [Formula: see text] or [Formula: see text]. We show these groups are solvable.

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