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Sets of Elements That Pairwise Generate a Linear Group by J.R. Britnell; A. Evseev; R.M. Guralnick; P.E. Holmes; A. Maróti is a Mathematics article available to read on EtoBox.

What is Sets of Elements That Pairwise Generate a Linear Group about?

Let G be any of the groups (P )GL(n, q), (P )SL (n, q). Define a (simple) graph Γ = Γ (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 Γ is equal to the chromatic number of Γ if n ≡ 2 (mod 4), or if n ≡ 2 (mod 4), q is odd and G = (P )SL (n, q). This work was motivated by a question of Blackburn.

Who reads Sets of Elements That Pairwise Generate a Linear Group?

Author

J.R. Britnell; A. Evseev; R.M. Guralnick; P.E. Holmes; A. Maróti

Publisher

Elsevier Science; Elsevier ; Elsevier Inc.; Elsevier BV (ISSN 0097-3165)

Published

2008

Language

EN

Field

Mathematics (Physical Sciences)