Sets of elements that pairwise generate a linear group

JR Britnell; A Evseev; RM Guralnick; PE Holmes; A Maroti

doi:10.1016/j.jcta.2007.07.002

Sets of elements that pairwise generate a linear group

JR Britnell, A Evseev, RM Guralnick, PE Holmes, A Maroti

School of Mathematics

Research output: Contribution to journal › Article (Academic Journal) › peer-review

32 Citations (Scopus)

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
Original language	English
Pages (from-to)	442 - 465
Number of pages	24
Journal	Journal of Combinatorial Theory, Series A
Volume	115, issue 3
DOIs	https://doi.org/10.1016/j.jcta.2007.07.002
Publication status	Published - Apr 2008

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Publisher: Elsevier

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title = "Sets of elements that pairwise generate a linear group",

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.",

author = "JR Britnell and A Evseev and RM Guralnick and PE Holmes and A Maroti",

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language = "English",

volume = "115, issue 3",

pages = "442 -- 465",

journal = "Journal of Combinatorial Theory, Series A",

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T1 - Sets of elements that pairwise generate a linear group

AU - Britnell, JR

AU - Evseev, A

AU - Guralnick, RM

AU - Holmes, PE

AU - Maroti, A

N1 - Publisher: Elsevier

PY - 2008/4

Y1 - 2008/4

N2 - 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.

AB - 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.

U2 - 10.1016/j.jcta.2007.07.002

DO - 10.1016/j.jcta.2007.07.002

M3 - Article (Academic Journal)

VL - 115, issue 3

SP - 442

EP - 465

JO - Journal of Combinatorial Theory, Series A

JF - Journal of Combinatorial Theory, Series A

ER -

Sets of elements that pairwise generate a linear group

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