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arXiv · 1804.10513

2-Parts of real class sizes

Hung P. Tong-Viet
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Abstract

We investigate the structure of finite groups whose non-central 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.

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Hung P. Tong-Viet. 2018-08-16. 2-Parts of real class sizes. https://doi.org/10.2140/ant.2018.12.2499

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