On the smallest simple, unipotent Bol loop

K. W. Johnson, J. D.H. Smith

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


Finite simple, unipotent Bol loops have recently been identified and constructed using group theory. However, the purely group-theoretical constructions of the actual loops are indirect, somewhat arbitrary in places, and rely on computer calculations to a certain extent. In the spirit of revisionism, this paper is intended to give a more explicit combinatorial specification of the smallest simple, unipotent Bol loop, making use of concepts from projective geometry and quasigroup theory along with the group-theoretical background. The loop has dual permutation representations on the projective line of order 5, with doubly stochastic action matrices.

Original languageEnglish (US)
Pages (from-to)790-798
Number of pages9
JournalJournal of Combinatorial Theory. Series A
Issue number6
StatePublished - Aug 2010

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics


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