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Graphs associated with the sporadic simple groups Fi₂₄ and BM

Our aim is to calculate some graphs associated with two of the larger sporadicsimple groups, Fi₂₄ and the Baby Monster. Firstly we calculate the point line collinearity graph for a maximal 2-local geometry of Fi₂₄. If T is such a geometry, then the point line collinearity graph G will be the graph whose vertices are the points in T, with any two vertices joined by an edge if and only if they are incident with a common line. We found that the graph has diameter 5 and we give its collapsed adjacency matrix. We also calculate part of the commuting involution graph, C, for the class 2C of the Baby Monster, whose vertex set is the conjugacy class 2C, with any two elements joined by an edge if and only if they commute. We have managed to place all vertices inside C whose product with a fixed vertex t does not have 2 power order, with all evidence pointing towards C having diameter 3.

Identiferoai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:538465
Date January 2011
CreatorsWright, Benjamin
ContributorsRowley, Peter ; Stohr, Ralph
PublisherUniversity of Manchester
Source SetsEthos UK
Detected LanguageEnglish
TypeElectronic Thesis or Dissertation
Sourcehttps://www.research.manchester.ac.uk/portal/en/theses/graphs-associated-with-the-sporadic-simple-groups-fi24-and-bm(dcdd493b-929d-4f91-a6bc-48c6b5fda3ba).html

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