The fixity of permutation groups

Jan Saxl, Aner Shalev

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


The fixity of a finite permutation group G is the maximal number of fixed points of a non-trivial element of G. We analyze the structure of non-regular permutation groups G with given fixity f. We show that if G is transitive and nilpotent, then it has a subgroup whose index and nilpotency class are both f-bounded.We also show that if G is primitive, then either it has a solublesubgroup of f-bounded index and derived length at most 4, or F*(G) is PSL(2, q) or Sz(q) in the natural permutation representations of degree q + 1, q2 + 1 respectively.

Original languageAmerican English
Pages (from-to)1122-1140
Number of pages19
JournalJournal of Algebra
Issue number3
StatePublished - 15 Jun 1995


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