Fixed points of elements of linear groups

Martin W. Liebeck; Aner Shalev

doi:10.1112/blms/bdr025

Fixed points of elements of linear groups

Martin W. Liebeck^*, Aner Shalev

^*Corresponding author for this work

Einstein Institute of Mathematics

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

3 Scopus citations

Abstract

We prove that for any finite group G, such that G/R(G)>120 (where R(G) is the soluble radical of G), and any finite-dimensional vector space V on which G acts, there is a non-identity element of G with fixed-point space of dimension at least 1/6 dim V. This bound is best possible.

Original language	American English
Pages (from-to)	897-900
Number of pages	4
Journal	Bulletin of the London Mathematical Society
Volume	43
Issue number	5
DOIs	https://doi.org/10.1112/blms/bdr025
State	Published - Oct 2011

Bibliographical note

Funding Information:
The authors were supported by an EPSRC grant. The second author holds the Miriam and Julius Vinik Chair in Mathematics, and is also supported by grants from the Israel Science Foundation and the ERC.

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10.1112/blms/bdr025

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AB - We prove that for any finite group G, such that G/R(G)>120 (where R(G) is the soluble radical of G), and any finite-dimensional vector space V on which G acts, there is a non-identity element of G with fixed-point space of dimension at least 1/6 dim V. This bound is best possible.

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Fixed points of elements of linear groups

Abstract

Bibliographical note

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