On Capable groups of order p^2q (original) (raw)

A group is said to be capable if it is the central factor of some group. In this paper, among other results we have characterized capable groups of order p 2 q, for any distinct primes p, q, which extends Theorem 1.2 of S. Rashid, N. H. Sarmin, A. Erfanian, and N. M. Mohd Ali, On the non abelian tensor square and capability of groups of order p 2 q, Arch. Math., 97 (2011), 299-306. We have also computed the number of distinct element centralizers of a group (finite or infinite) with central factor of order p 3 , which extends Proposition 2.