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.
Bibliographical noteFunding Information:
The authors are grateful for the support of an EPSRC grant EP/H018891/1 . The second author acknowledges the support of grants from the Israel Science Foundation ( 2008194 ) and ERC ( 247034 ).
© 2014 Elsevier Inc.
- Fixed points
- Involution fixity
- Permutation groups
- Primitive permutation groups