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Bases of primitive linear groups

โœ Scribed by Martin W. Liebeck; Aner Shalev

Book ID
104140273
Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
168 KB
Volume
252
Category
Article
ISSN
0021-8693

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โœฆ Synopsis

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.

๐Ÿ“œ SIMILAR VOLUMES

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A well-developed branch of asymptotic group theory studies the properties of classes of linear and permutation groups as functions of their degree. We refer to the surveys of Cameron [4] and Pyber [17,18] and the recent paper by Pyber and Shalev [19] for a detailed exposition of this subject. In thi