Fixed points of elements of linear groups

Martin W. Liebeck*, Aner Shalev

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


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 languageAmerican English
Pages (from-to)897-900
Number of pages4
JournalBulletin of the London Mathematical Society
Issue number5
StatePublished - 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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