On Thompson Problem

Rulin Shen; Wujie Shi; Feng Tang

On Thompson Problem

Group Theory 2023-09-19 v2

Authors: Rulin Shen , Wujie Shi , Feng Tang

Abstract

In 1987, the second author of this paper reported his conjecture, all finite simple groups $S$ can be characterized uniformly using the order of $S$ and the set of element orders in $S$ , to Prof. J. G. Thompson. In their communications, Thompson posed his problem about the judgment of solvability of finite groups $G$ . In this paper we give a positive answer for Thompson's problem if the prime graph of $G$ is not connection.

Keywords

finite group theory group theory wreath product of groups

Cite

@article{arxiv.2308.07183,
  title  = {On Thompson Problem},
  author = {Rulin Shen and Wujie Shi and Feng Tang},
  journal= {arXiv preprint arXiv:2308.07183},
  year   = {2023}
}

Comments

8 pages

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