n-capability of A-groups

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Chakaneh Marzieh; Kayvanfar Saeed; Hatamian Rasoul

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Journal Paper

Paper Information

Journal: Mathematics Interdisciplinary Research Year:2020 | Volume:5 | Issue:4 Page(s): 345-353

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Information Journal Paper

Title

n-capability of A-groups

Author(s)

Chakaneh Marzieh | Kayvanfar Saeed | Hatamian Rasoul | Issue Writer Certificate

Keywords

n-Capable group

Sylow subgroup

Frattini subgroup

Abstract

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.

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