Steiner loops satisfying the statement of Moufang's theorem

Maria De Lourdes Merlini Giuliani, Giliard Souza Dos Anjos, Charles Colbourn

Research output: Contribution to journalArticle

Abstract

Andrew Rajah posed at the Loops'11 Conference in Trest, Czech Republic, the following conjecture: Is every variety of loops that satisfies Moufang's theorem contained in the variety of Moufang loops? This paper is motivated by that problem. We give a partial answer to this question and present two types of Steiner loops, one that satisfies Moufang's theorem and another that does not, and neither is Moufang loop.

Original languageEnglish (US)
Pages (from-to)103-108
Number of pages6
JournalQuasigroups and Related Systems
Volume24
Issue number1
StatePublished - 2016

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Moufang Loop
Theorem
Partial

Keywords

  • Moufang loop
  • Moufang theorem
  • Steiner loop

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Algebra and Number Theory

Cite this

De Lourdes Merlini Giuliani, M., Dos Anjos, G. S., & Colbourn, C. (2016). Steiner loops satisfying the statement of Moufang's theorem. Quasigroups and Related Systems, 24(1), 103-108.

Steiner loops satisfying the statement of Moufang's theorem. / De Lourdes Merlini Giuliani, Maria; Dos Anjos, Giliard Souza; Colbourn, Charles.

In: Quasigroups and Related Systems, Vol. 24, No. 1, 2016, p. 103-108.

Research output: Contribution to journalArticle

De Lourdes Merlini Giuliani, M, Dos Anjos, GS & Colbourn, C 2016, 'Steiner loops satisfying the statement of Moufang's theorem', Quasigroups and Related Systems, vol. 24, no. 1, pp. 103-108.
De Lourdes Merlini Giuliani M, Dos Anjos GS, Colbourn C. Steiner loops satisfying the statement of Moufang's theorem. Quasigroups and Related Systems. 2016;24(1):103-108.
De Lourdes Merlini Giuliani, Maria ; Dos Anjos, Giliard Souza ; Colbourn, Charles. / Steiner loops satisfying the statement of Moufang's theorem. In: Quasigroups and Related Systems. 2016 ; Vol. 24, No. 1. pp. 103-108.
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