2-parts of real class sizes

Hung P. Tong-Viet

doi:10.2140/ant.2018.12.2499

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Home > Journals > Algebra Number Theory > Volume 12 > Issue 10 > Article

2018 2-parts of real class sizes

Hung P. Tong-Viet

Algebra Number Theory 12(10): 2499-2514 (2018). DOI: 10.2140/ant.2018.12.2499

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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.