Fixed points of elements of linear groups

Martin W. Liebeck; Aner Shalev

doi:https://doi.org/10.1112/blms/bdr025

Fixed points of elements of linear groups

Martin W. Liebeck, Aner Shalev

Einstein Institute of Mathematics

The Hebrew University of Jerusalem

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

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	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

All Science Journal Classification (ASJC) codes

Mathematics(all)

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Cite this

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title = "Fixed points of elements of linear groups",

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.",

author = "Liebeck, {Martin W.} and Aner Shalev",

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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N2 - 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.

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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M3 - Article

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SP - 897

EP - 900

JO - Bulletin of the London Mathematical Society

JF - Bulletin of the London Mathematical Society

IS - 5

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Fixed points of elements of linear groups

Abstract

All Science Journal Classification (ASJC) codes

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