The generalised Fitting subgroup of a profinite group

2009/04/02 by Colin Reid, Reid, Colin
Mathematics · #FOS: Mathematics #Group Theory (math.GR) #math.GR

paper · pdf · doi:10.48550/arxiv.0904.0424

17 pages

arxiv created 2009/04/02 · arxiv updated 2009/12/01

Abstract

The generalised Fitting subgroup of a finite group is the group generated by all subnormal subgroups that are either nilpotent or quasisimple. The importance of this subgroup in finite group theory stems from the fact that it always contains its own centraliser, so that any finite group is an abelian extension of a group of automorphisms of its generalised Fitting subgroup. We define a class of profinite groups which generalises this phenomenon, and explore some consequences for the structure of profinite groups.

Related

• Generalized Fitting subgroups of finite groups
• Fitting like subgroups of finite groups
• Some aspects of profinite group theory
• Irreducible induction and nilpotent subgroups in finite groups
• On some applications of Fitting like subgroups of finite groups