%0 Journal Article
%T n-capability of A-groups
%J Mathematics Interdisciplinary Research
%I University of Kashan
%Z 2538-3639
%A Chakaneh, Marzieh
%A Kayvanfar, Saeed
%A Hatamian, Rasoul
%D 2020
%\ 12/01/2020
%V 5
%N 4
%P 345-353
%! n-capability of A-groups
%K n-Capable group
%K Sylow subgroup
%K Frattini subgroup
%R 10.22052/mir.2020.240334.1251
%X 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 p2q, 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.
%U https://mir.kashanu.ac.ir/article_110821_0abe1545736a161f9fd287d64f272d75.pdf