On the intersections of solvable Hall subgroups in finite groups

E. P. Vdovin; V. I. Zenkov

On the intersections of solvable Hall subgroups in finite groups

Group Theory 2010-08-17 v1 Geometric Topology

Authors: E. P. Vdovin , V. I. Zenkov

Abstract

In the paper we consider the following conjecture: if a finite group $G$ possesses a solvable $\pi$ -Hall subgroup $H$ , then there exist elements $x,y,z,t\in G$ such that the identity $H\cap H^x\cap H^y\cap H^z\cap H^t=O_\pi(G)$ holds. The minimal counter example is shown to be an almost simple group of Lie type.

Keywords

finite group theory topological groups finite groups

Cite

@article{arxiv.0812.3204,
  title  = {On the intersections of solvable Hall subgroups in finite groups},
  author = {E. P. Vdovin and V. I. Zenkov},
  journal= {arXiv preprint arXiv:0812.3204},
  year   = {2010}
}

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