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.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:549644 |
| Date | January 2012 |
| Creators | Ballantyne, John Joseph |
| Contributors | Rowley, Peter |
| Publisher | University of Manchester |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | https://www.research.manchester.ac.uk/portal/en/theses/local-fusion-graphs-of-finite-groups(131e11a2-2ca6-478e-b8d9-119a78de8935).html |
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