2-Blocks with Homocyclic Defect Group and Inertial Quotient Containing a Singer Cycle

Abstract

In this thesis we classify several families of blocks whose inertial quotient contains a Singer cycle. In particular, we consider 2-blocks of a finite group, whose defect group is elementary abelian or homocyclic, and whose inertial quotient contains a Singer cycle - an element of order one less than a power of two. The action of the inertial quotient on the defect group can be well-understood, allowing a classification of such blocks up to basic Morita equivalence in many cases.

Date of Award	31 Dec 2020
Original language	English
Awarding Institution	The University of Manchester
Supervisor	Charles Eaton (Supervisor) & John Stafford (Supervisor)