Sets of elements that pairwise generate a linear group
نویسندگان
چکیده
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. We prove that if the dimension n is at least 12 and not congruent to 2 modulo 4, then the maximum size of a complete subgraph in Γ is equal to the chromatic number of Γ. This work was motivated by a question of Blackburn.
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a Department of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, UK b School of Mathematical Sciences, Queen Mary, University of London, Mile End Road, London E1 4NS, UK c Department of Mathematics, University of Southern California, Los Angeles, CA 90089-2532, USA d DPMMS, Centre for Mathematical Sciences, University of Cambridge, Cambridge CB3 0BW, UK e Alfréd Rényi Insti...
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ورودعنوان ژورنال:
- J. Comb. Theory, Ser. A
دوره 115 شماره
صفحات -
تاریخ انتشار 2008