n-capability of a-groups

Following p. hall a soluble group whose sylow subgroups are all abelian is called agroup. the purpose of this article is to give a new and shorter proof for a criterion on the capability of agroups of order p^2q, where p and q are distinct primes. subsequently we give a sufficient condition for ncapability 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.