On the fixity of linear groups

Aner Shalev

doi:10.1112/plms/s3-68.2.265

On the fixity of linear groups

Aner Shalev^*

^*Corresponding author for this work

Einstein Institute of Mathematics

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

16 Scopus citations

Abstract

The fixity of a linear group G GL(V) is defined to be the maximal dimension of a centraliser C_v(g) for with g 1. We study the structure of finite non-modular linear groups of given fixity f. Our results may be regarded as an extension of the theory of Frobenius complements on the one hand, and of Jordan’s classical theorem on finite subgroups of GL_n(C) on the other. As an application we show that if G is a group of automorphisms of a finite group H, and each non-trivial element of G fixes at most f points of H, then G has a soluble subgroup of derived length at most 3 whose index is bounded above in terms of f alone.

Original language	English
Pages (from-to)	265-293
Number of pages	29
Journal	Proceedings of the London Mathematical Society
Volume	s3-68
Issue number	2
DOIs	https://doi.org/10.1112/plms/s3-68.2.265
State	Published - Mar 1994

Bibliographical note

Funding Information:
The author is grateful to the Mathematics Research Section of the Australian National University for its kind hospitality while this work was carried out. 1991 Mathematics Subject Classification: 20D99, 20G15.

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10.1112/plms/s3-68.2.265

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On the fixity of linear groups

Abstract

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