## 2012.8: Local Fusion Graphs of Finite Groups

2012.8:
John J Ballantyne
(2011)
*Local Fusion Graphs of Finite Groups.*
PhD 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 (PhD) |
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Uncontrolled Keywords: | finite group, involution, graph, centraliser |

Subjects: | MSC 2000 > 20 Group theory and generalizations |

MIMS number: | 2012.8 |

Deposited By: | Mr John Ballantyne |

Deposited On: | 08 January 2012 |

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