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arXiv · 1803.01717

Real class sizes

Hung P. Tong-Viet
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Abstract

In this paper, we study the structures of finite groups using some arithmetic conditions on the sizes of real conjugacy classes. We prove that a finite group is solvable if the prime graph on the real class sizes of the group is disconnected. Moreover, we show that if the sizes of all non-central real conjugacy classes of a finite group $G$ have the same $2$-part and the Sylow $2$-subgroup of $G$ satisfies certain condition, then $G$ is solvable.

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Hung P. Tong-Viet. 2018-03-01. Real class sizes. https://arxiv.org/abs/1803.01717

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