On Capable groups of order p²q

2019/11/08 by Sekhar Jyoti Baishya, Baishya, Sekhar Jyoti
Mathematics · #FOS: Mathematics #Group Theory (math.GR) #math.GR

paper · pdf · doi:10.48550/arxiv.1911.03279

arxiv created 2020/01/26 · arxiv updated 2020/01/28

Abstract

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 p²q, for any distinct primes p, q, which extends Theorem 1.2 of S. Rashid, N. H. Sarmin, A. Erfanian, and N. M. Mohd Ali, \em On the non abelian tensor square and capability of groups of order p²q, 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 p³, which extends Proposition 2.10 of S. M. Jafarian Amiri, H. Madadi and H. Rostami, \em On F-groups with the central factor of order p⁴, Math. Slovaca, 67 (5) (2017), 1147--1154.

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