The Generalised Pro-Fitting Subgroup of a Profinite Group

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.

Key Words:

• Group theory
• Profinite groups
• Sylow theory

2010 Mathematics Subject Classification:

• 20E18

ACKNOWLEDGMENTS

This article is based on results obtained by the author while under the supervision of Robert Wilson at Queen Mary, University of London (QMUL). I would also like to thank Charles Leedham-Green for his advice and guidance during my doctoral studies.

Notes

Communicated by A. Olshanskii