Bounds on finite quasiprimitive permutation groups

Cheryl E. Praeger*, Aner Shalev

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


A permutation group is said to be quasiprimitive if every nontrivial normal subgroup is transitive. Every primitive permutation group is quasiprimitive, but the converse is not true. In this paper we start a project whose goal is to check which of the classical results on finite primitive permutation groups also holds for quasiprimitive ones (possibly with some modifications). The main topics addressed here are bounds on order, minimum degree and base size, as well as groups containing special p-elements. We also pose some problems for further research.

Original languageAmerican English
Pages (from-to)243-258
Number of pages16
JournalJournal of the Australian Mathematical Society
Issue number2
StatePublished - Oct 2001

Bibliographical note

Funding Information:
This paper forms part of an Australian Research Council large grant project of the first author. The second author acknowledges the support of the Israel Science Foundation, founded by the Israeli Academy of Science and Humanities. © 2001 Australian Mathematical Society 0263-6115/2001 $A2.00 + 0.00


  • Primitive permutation group
  • Quasiprimitive permutation group


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