On the smallest simple, unipotent Bol loop

Kenneth Johnson, J. D.H. Smith

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

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
Volume117
Issue number6
DOIs
StatePublished - Aug 1 2010

Fingerprint

Bol Loop
Group theory
Specifications
Permutation Representation
Quasigroup
Projective geometry
Geometry
Group Theory
Specification
Line
Arbitrary

All Science Journal Classification (ASJC) codes

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

Cite this

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On the smallest simple, unipotent Bol loop. / Johnson, Kenneth; Smith, J. D.H.

In: Journal of Combinatorial Theory. Series A, Vol. 117, No. 6, 01.08.2010, p. 790-798.

Research output: Contribution to journalArticle

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