The existence of pronormal π-Hall subgroups in E_π-groups

2015/04/11 by D. O. Revin, E. P. Vdovin, Revin, D. O. +1
Mathematics · #FOS: Mathematics #Group Theory (math.GR) #math.GR

paper · pdf · doi:10.48550/arxiv.1504.02834

arxiv created 2015/04/16 · arxiv updated 2015/04/17

Abstract

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

Related

• Frattini Argument for Hall subgroups
• On the Pronormality of Subgroups of Odd Index in Finite Simple Groups
• On the heritability of the Hall property D_π by overgroups of π-Hall subgroups
• A generalization of the Arad--Ward theorem on Hall subgroups
• A Criterion for the Existence of a Solvable π-Hall Subgroup in a Finite Group