On the intersections of solvable Hall subgroups in finite groups

Details On the intersections of solvable Hall subgroups in finite groups On the intersections of solvable Hall subgroups in finite groups

2008-12-17

arxiv.org/abs/0812.3204v1

Proc. Stekl. Inst. Math. Suppl. 3, 2009, 234-243

Mathematics

Group Theory

Scientific paper

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.

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