The existence of pronormal $\pi$-Hall subgroups in $E_\pi$-groups

D. O. Revin; E. P. Vdovin

The existence of pronormal $\pi$-Hall subgroups in $E_\pi$-groups

Group Theory 2015-04-17 v2

Authors: D. O. Revin , E. P. Vdovin

Abstract

A subgroup $H$ of a group $G$ is called {\it pronormal}, if for every $g\in G$ subgroups $H$ and $H^g$ are conjugate in $\langle H, H^g\rangle$ . It is proven that if a finite group $G$ possesses a $\pi$ -Hall subgroup for a set of primes $\pi$ , the every its normal subgroup (in particular, $G$ itself) possesses a $\pi$ -Hall subgroup that is pronormal in~ $G$ .

Keywords

pronormal subgroups pi-Hall subgroups finite groups conjugate subgroups E_pi-groups

Cite

@article{arxiv.1504.02834,
  title  = {The existence of pronormal $\pi$-Hall subgroups in $E_\pi$-groups},
  author = {D. O. Revin and E. P. Vdovin},
  journal= {arXiv preprint arXiv:1504.02834},
  year   = {2015}
}

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