publication . Article . 2008

Sets of elements that pairwise generate a linear group

A. Evseev; John R. Britnell; Attila Maróti; Robert M. Guralnick; P. E. Holmes;
Open Access
  • Published: 01 Apr 2008 Journal: Journal of Combinatorial Theory, Series A, volume 115, issue 3, pages 442-465 (issn: 0097-3165, Copyright policy)
  • Publisher: Elsevier BV
Abstract
Let G be any of the groups (P)GL(n,q), (P)SL(n,q). Define a (simple) graph @[email protected](G) on the set of elements of G by connecting two vertices by an edge if and only if they generate G. Suppose that n is at least 12. Then the maximum size of a complete subgraph in @C is equal to the chromatic number of @C if [email protected]?2(mod4), or if n=2(mod4), q is odd and G=(P)SL(n,q). This work was motivated by a question of Blackburn.
Subjects
free text keywords: Theoretical Computer Science, Computational Theory and Mathematics, Discrete Mathematics and Combinatorics, General linear group, Covering, Pairwise generating set, Maximum size, Combinatorics, Discrete mathematics, Graph, Pairwise comparison, Chromatic scale, Mathematics, Vertex (geometry), If and only if
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