A conjugacy criterion for Hall subgroups in finite groups

Abstract

A finite group $G$ is said to satisfy $C_{\pi }$ for a set of primes $\pi$, if $G$ possesses exactly one class of conjugate $\pi$-Hall subgroups. In the paper we obtain a criterion for a finite group $G$ to satisfy $C_{\pi }$ in terms of a normal series of the group.

Appear in Siberian Mathematical Journal, vol. 51 (2010), No3.

Cited by in corpus (1)

• Pronormality of Hall subgroups in finite simple groups