Transitive fusion systems over a class of finite p-groups

Rui Gao; Heguo Liu; Xingzhong Xu; Sheng Yang

Transitive fusion systems over a class of finite p-groups

Group Theory 2024-12-05 v2

Authors: Rui Gao , Heguo Liu , Xingzhong Xu , Sheng Yang

Abstract

Let $p$ be an odd prime and $S$ a nonabelian finite $p$ -group. In [9, 10], they proposed the following conjecture: if $\mathcal{F}$ be a transitive fusion system over a finite $p$ -group $S$ , then $S$ is either extraspecial of order $p^{3}$ or elementary abelian. In this note, we use an easy method to prove that this conjecture holds when the $p$ -rank of $S$ is 2.

Keywords

fusion system finite p-groups transitive fusion system extraspecial group elementary abelian p-rank

Cite

@article{arxiv.2412.01294,
  title  = {Transitive fusion systems over a class of finite p-groups},
  author = {Rui Gao and Heguo Liu and Xingzhong Xu and Sheng Yang},
  journal= {arXiv preprint arXiv:2412.01294},
  year   = {2024}
}

Comments

Prof. B. Sambale tells us that this result is trivial

Transitive fusion systems over a class of finite p-groups

Abstract

Keywords

Cite

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