Ballantyne, John J
(2011)
*Local Fusion Graphs of Finite Groups.*
Doctoral thesis, Manchester Institute for Mathematical Sciences, The University of Manchester.

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## 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 and y are not equal 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 when G is a finite simple group. We also present a computational algorithm regarding centralisers of involutions, which makes use of local fusion graphs.

Item Type: | Thesis (Doctoral) |
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Uncontrolled Keywords: | finite group, involution, graph, centraliser |

Subjects: | MSC 2010, the AMS's Mathematics Subject Classification > 20 Group theory and generalizations |

Depositing User: | Dr John Ballantyne |

Date Deposited: | 08 Jan 2012 |

Last Modified: | 20 Oct 2017 14:13 |

URI: | http://eprints.maths.manchester.ac.uk/id/eprint/1752 |

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