Invariable generation and the Chebotarev invariant of a finite group

W. M. Kantor*, A. Lubotzky, A. Shalev

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

34 Scopus citations


A subset S of a finite group G invariably generates G if G=〈sg(s)|s∈S〉 for each choice of g(s)∈G, s∈S. We give a tight upper bound on the minimal size of an invariable generating set for an arbitrary finite group G. In response to a question in Kowalski and Zywina (2010) [KZ] we also bound the size of a randomly chosen set of elements of G that is likely to generate G invariably. Along the way we prove that every finite simple group is invariably generated by two elements.

Original languageAmerican English
Pages (from-to)302-314
Number of pages13
JournalJournal of Algebra
Issue number1
StatePublished - 15 Dec 2011

Bibliographical note

Funding Information:
✩ The authors acknowledge partial support from NSF grant DMS 0753640 (W.M.K.), ERC Advanced Grants 226135 (A.L.) and 247034 (A.S.), and ISF grant 754/08 (A.L. and A.S.). The first author is grateful for the warm hospitality of the Hebrew University while this paper was being written. * Corresponding author. E-mail addresses: (W.M. Kantor), (A. Lubotzky), (A. Shalev).


  • Chebotarev invariant
  • Invariable generation
  • Simple group


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