Real class sizes

Hung P. Tong-Viet

Real class sizes

Group Theory 2018-03-06 v1

Authors: Hung P. Tong-Viet

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.

Keywords

conjugacy classes in groups finite group theory group theory

Cite

@article{arxiv.1803.01717,
  title  = {Real class sizes},
  author = {Hung P. Tong-Viet},
  journal= {arXiv preprint arXiv:1803.01717},
  year   = {2018}
}

Comments

13 pages

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