## Abstract

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 |
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Original language | English |

Pages (from-to) | 442 - 465 |

Number of pages | 24 |

Journal | Journal of Combinatorial Theory, Series A |

Volume | 115, issue 3 |

DOIs | |

Publication status | Published - Apr 2008 |