Mathematics Interdisciplinary Research, Volume (5), No (4), Year (2020-12) , Pages (353-345)

Title : ( n-Capability of A-Groups )

Authors: Marzieh Chakaneh , Saeed Kayvanfar , Rasoul Hatamian ,

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Following P. Hall a soluble group whose Sylow subgroups are all abelian is called A-group. The purpose of this article is to give a new and shorter proof for a criterion on the capability of A-groups of order p^2q, where p and q are distinct primes. Subsequently we give a sufficient condition for n-capability of groups having the property that their center and derived subgroups have trivial intersection, like the groups with trivial Frattini subgroup and A-groups. An interesting necessary and sufficient condition for capability of the A-groups of square free order will be also given.


, n-capable group, Sylow subgroup, Frattini subgroup.
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author = {Chakaneh, Marzieh and Kayvanfar, Saeed and Rasoul Hatamian},
title = {n-Capability of A-Groups},
journal = {Mathematics Interdisciplinary Research},
year = {2020},
volume = {5},
number = {4},
month = {December},
issn = {2538-3639},
pages = {353--345},
numpages = {-8},
keywords = {n-capable group; Sylow subgroup; Frattini subgroup.},


%0 Journal Article
%T n-Capability of A-Groups
%A Chakaneh, Marzieh
%A Kayvanfar, Saeed
%A Rasoul Hatamian
%J Mathematics Interdisciplinary Research
%@ 2538-3639
%D 2020