Finite 2-groups of Class 2 with Specific Automorphism Group
Group Theory
2012-12-05 v1
Abstract
In this paper we classify all finite 2-groups of class 2 for which every automorphism of order 2 leaving the Frattini subgroup elementwise fixed is inner. We prove that every such group G is isomorphic to Q(n; r) = <a, b| a^{2n}= b^{2r}= 1; a^2^{n-r}= [a, b]> for some positive integers r; n such that 2 < 2r <= n; and every automorphism of Q(n; r) of order 2 leaving the Frattini subgroup elementwise fixed is inner.
Cite
@article{arxiv.1212.0799,
title = {Finite 2-groups of Class 2 with Specific Automorphism Group},
author = {A. Abdollahi and M. Ahmadi and S. M. Ghoraishi},
journal= {arXiv preprint arXiv:1212.0799},
year = {2012}
}