Infinite 3/2-generated groups

Scott Harper, Casey Donoven

Research output: Contribution to journalArticle (Academic Journal)peer-review

4 Citations (Scopus)
49 Downloads (Pure)


Every finite simple group can be generated by two elements, and Guralnick and Kantor proved that, moreover, every nontrivial element is contained in a generating pair. Groups with this property are said to be 3 2-generated. Thompson’s group V was the first finitely presented infinite simple group to be discovered. The Higman–Thompson groups Vn and the Brin–Thompson groups mV are two families of finitely presented groups that generalise V. In this paper, we prove that all of the groups Vn, V0 n and mV are 3 2-generated. As far as the authors are aware, the only previously known examples of infinite noncyclic 3 2-generated groups are the pathological Tarski monsters. We conclude with several open questions motivated by our results.
Original languageEnglish
Number of pages17
JournalBulletin of the London Mathematical Society
Early online date10 Jun 2020
Publication statusPublished - 13 Aug 2020


  • 20F05 (primary)
  • 20B22
  • 20E32 (secondary)


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