p-minimal subgroups of the symmetric groups and alternating groups.

Abstract

A subgroup of a group is p-minimal if the normalizer of a Sylow subgroup of the group is contained in a unique maximal subgroup of it. For p an odd prime, this thesis derives a detailed and explicit description of all the p-minimal subgroups of the symmetric groups and alternating groups. The proof of this description depends on the classification of finite simple groups. Also conditions where the construction can be proved, without the classification, for a given prime are considered.

Date of Award	22 Nov 2021
Original language	English
Awarding Institution	The University of Manchester
Supervisor	Peter Rowley (Main Supervisor) & Yuri Bazlov (Co Supervisor)