English

A group theoretic proof of Frobenius' theorem

General Mathematics 2020-11-23 v4

Abstract

Let G be a Frobenius group with the Frobenius kernel N. Applying character theory, G. Frobenius proved that N was a normal subgroup of G in the year 1901. This is a celebrated application of the character theory of finite groups. In this note, we give a character-free proof of the result, which is a well-known problem in the theory of finite groups.

Keywords

Cite

@article{arxiv.2002.02103,
  title  = {A group theoretic proof of Frobenius' theorem},
  author = {Liguo He and Congru Xu},
  journal= {arXiv preprint arXiv:2002.02103},
  year   = {2020}
}

Comments

The proof of Lemma 2.7 is false

R2 v1 2026-06-23T13:32:40.477Z