A note on Flavell's theorem associated with Frobenius groups
Group Theory
2022-12-21 v1
Abstract
Let G be a Frobenius group with the Frobenius kernel K. Suppose that G contains a nontrival subgroup D \subseteq K such that the normalizer N_G(D) \not\subseteq K. When D is no 2-group, Flavell proved, without using character theory, that K is a subgroup of G. Based on this result, we further prove that K is a subgroup when D is a 2-group.
Cite
@article{arxiv.2212.10480,
title = {A note on Flavell's theorem associated with Frobenius groups},
author = {Liguo He and Gang Zhu},
journal= {arXiv preprint arXiv:2212.10480},
year = {2022}
}
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10 pages