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Structure of the $Fi_{24}^{\prime }$ maximal $2$-local geometry point-line collinearity graph

Part of: Graph theory Structure and classification of infinite or finite groups

Published online by Cambridge University Press:  01 March 2016

Peter Rowley  and
Ben Wright
Peter Rowley
Affiliation:
The School of Mathematics, Alan Turing Building, The University of Manchester, Oxford Road, Manchester M13 9PL, United Kingdom email [email protected]
Ben Wright
Affiliation:
The School of Mathematics, Alan Turing Building, The University of Manchester, Oxford Road, Manchester M13 9PL, United Kingdom email [email protected]

Abstract

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The point-line collinearity graph ${\mathcal{G}}$ of the maximal 2-local geometry for the largest simple Fischer group, $Fi_{24}^{\prime }$, is extensively analysed. For an arbitrary vertex $a$ of ${\mathcal{G}}$, the $i\text{th}$-disc of $a$ is described in detail. As a consequence, it follows that ${\mathcal{G}}$ has diameter $5$. The collapsed adjacency matrix of ${\mathcal{G}}$ is given as well as accompanying computer files which contain a wealth of data about ${\mathcal{G}}$.

Supplementary materials are available with this article.

MSC classification

Primary: 05C25: Graphs and abstract algebra (groups, rings, fields, etc.) 20E32: Simple groups
Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 19 , Issue 1 , 2016 , pp. 105 - 154
Copyright
© The Author(s) 2016 

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