Title : ( On the Groups with Trivial Frattini Subgroups )
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Abstract
In 2012, Guo and Gong prove that if G is a finite non-abelian group with -G- = 1, then jG : Z-G-j < jG′jjU-G-j, in which U-G- is the nilpotent residual of G. In the present work, we prove that the assumption of finite- ness of the group can be omitted. Moreover, we state some properties of groups G for which n+1-G- \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\ Zn-G- = 1 in the spacial case -G- = 1.
Keywords
Frattini subgroup; Upper and lower central series
@inproceedings{paperid:1073996,
author = {},
title = {On the Groups with Trivial Frattini Subgroups},
booktitle = {یازدهمین کنفرانس نظریه گروه ها},
year = {2019},
location = {yazd, IRAN},
keywords = {Frattini subgroup; Upper and lower central series},
}
%0 Conference Proceedings
%T On the Groups with Trivial Frattini Subgroups
%A
%J یازدهمین کنفرانس نظریه گروه ها
%D 2019
