Title : ( ON THE CONVERSE OF BAER\\\'S THEOREM FOR GENERALIZATIONS OF GROUPS WITH TRIVIAL FRATTINI SUBGROUPS )
Authors: Yasaman Taghavi , Saeed Kayvanfar , Marzieh Chakaneh ,
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Abstract
In 2012, Guo and Gong proved that if G is a nite nonabelian group with (G) = 1, then jG : Z(G)j < jG ′jjU(G)j, in which U(G) is the nilpotent residual of G. We show that the assumption of niteness of the group can be omitted. Moreover, we investigate converse of Schur and Baer\\\\\\\\\\\\\\\'s theorems for groups that can be seen as generalizations of groups with trivial Frattini subgroups and state some properties of n-isoclinism families of these groups. 1.
Keywords
, Baer\\\\\\\\\\\\\\\'s theorem, Frattini subgroup, Upper and lower central series.
@article{paperid:1074420,
author = {Taghavi, Yasaman and Kayvanfar, Saeed and Chakaneh, Marzieh},
title = {ON THE CONVERSE OF BAER\\\'S THEOREM FOR GENERALIZATIONS OF GROUPS WITH TRIVIAL FRATTINI SUBGROUPS},
journal = {Algebraic Structures and Their Applications},
year = {2019},
volume = {6},
number = {1},
month = {May},
issn = {2382-9761},
pages = {141--150},
numpages = {9},
keywords = {Baer\\\\\\\\\\\\\\\'s theorem; Frattini subgroup; Upper and lower central series.},
}
%0 Journal Article
%T ON THE CONVERSE OF BAER\\\'S THEOREM FOR GENERALIZATIONS OF GROUPS WITH TRIVIAL FRATTINI SUBGROUPS
%A Taghavi, Yasaman
%A Kayvanfar, Saeed
%A Chakaneh, Marzieh
%J Algebraic Structures and Their Applications
%@ 2382-9761
%D 2019
