On fixed points of elements in primitive permutation groups

Martin W. Liebeck*, Aner Shalev

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


The fixity of a finite permutation group is the maximal number of fixed points of a non-identity element. We study the fixity of primitive groups of degree n, showing that apart from a short list of exceptions, the fixity of such groups is at least n1/6. We also prove that there is usually an involution fixing at least n1/6 points.

Original languageAmerican English
Pages (from-to)438-459
Number of pages22
JournalJournal of Algebra
StatePublished - 1 Jan 2015

Bibliographical note

Publisher Copyright:
© 2014 Elsevier Inc.


  • Fixed points
  • Fixity
  • Involution fixity
  • Involutions
  • Permutation groups
  • Primitive permutation groups


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