Local Fusion Graphs of Finite Groups

Abstract

Let G be a group, with X a G-conjugacy class of involutions. The local fusion graph F(G,X) has X as its vertex set, with vertices x, y in X joined by an edge if, and only if, x is not equal to y and the order of the product xy is odd. In this thesis we study these, and other related graphs, for a variety of finite groups, paying particular attention to the cases where G is a finite group. We also present a computational algorithm regarding centralisers of involutions, which makes use of local fusion graphs.

Date of Award	31 Dec 2012
Original language	English
Awarding Institution	The University of Manchester
Supervisor	Peter Rowley (Supervisor)