2-parts of real class sizes

Tong-Viet, Hung

doi:10.2140/ant.2018.12.2499

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2-parts of real class sizes

Hung P. Tong-Viet

Vol. 12 (2018), No. 10, 2499–2514

DOI: 10.2140/ant.2018.12.2499

Abstract

We investigate the structure of finite groups whose noncentral real class sizes have the same $2$ -part. In particular, we prove that such groups are solvable and have $2$ -length one. As a consequence, we show that a finite group is solvable if it has two real class sizes. This confirms a conjecture due to G. Navarro, L. Sanus and P. Tiep.

Keywords

real conjugacy classes, involutions, $2$-parts, quasisimple groups

Mathematical Subject Classification 2010

Primary: 20E45

Secondary: 20D10

Milestones

Received: 12 May 2018

Revised: 14 August 2018

Accepted: 15 August 2018

Published: 1 February 2019

Authors

Hung P. Tong-Viet
Department of Mathematical Sciences Binghamton University Binghamton, NY 13902-6000 United States

Vol. 12, No. 10, 2018