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 , or if , q is odd and G=(P)SL(n,q). This work was motivated by a question of Blackburn.
|Translated title of the contribution||Sets of elements that pairwise generate a linear group|
|Pages (from-to)||442 - 465|
|Number of pages||24|
|Journal||Journal of Combinatorial Theory, Series A|
|Volume||115, issue 3|
|Publication status||Published - Apr 2008|