Vol. 12, No. 10, 2018

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2-parts of real class sizes

Hung P. Tong-Viet

Vol. 12 (2018), No. 10, 2499–2514
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