Bases of primitive linear groups

Martin W. Liebeck; Aner Shalev

doi:10.1016/S0021-8693(02)00001-7

Bases of primitive linear groups

Martin W. Liebeck^*
, Aner Shalev

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

25 Scopus citations

Abstract

Let V be a finite vector space and G ≤ GL(V) a linear group. A base of G is a set of vectors whose pointwise stabiliser in G is trivial. We prove that if G is irreducible and primitive on V, then G has a base of size at most 18 log G/log V + c, where c is an absolute constant. This verifies part of a conjecture of Pyber on base sizes of primitive permutation groups.

Original language	English
Pages (from-to)	95-113
Number of pages	19
Journal	Journal of Algebra
Volume	252
Issue number	1
DOIs	https://doi.org/10.1016/S0021-8693(02)00001-7
State	Published - 1 Jun 2002

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AB - Let V be a finite vector space and G ≤ GL(V) a linear group. A base of G is a set of vectors whose pointwise stabiliser in G is trivial. We prove that if G is irreducible and primitive on V, then G has a base of size at most 18 log G/log V + c, where c is an absolute constant. This verifies part of a conjecture of Pyber on base sizes of primitive permutation groups.

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Bases of primitive linear groups

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