Bases of primitive linear groups

Martin W. Liebeck*, Aner Shalev

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

21 Scopus citations


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 languageAmerican English
Pages (from-to)95-113
Number of pages19
JournalJournal of Algebra
Issue number1
StatePublished - 1 Jun 2002


Dive into the research topics of 'Bases of primitive linear groups'. Together they form a unique fingerprint.

Cite this