### 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 language | English (US) |
---|---|

Pages (from-to) | 103-108 |

Number of pages | 6 |

Journal | Quasigroups and Related Systems |

Volume | 24 |

Issue number | 1 |

State | Published - 2016 |

### Fingerprint

### Keywords

- Moufang loop
- Moufang theorem
- Steiner loop

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Algebra and Number Theory

### Cite this

*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.

Research output: Contribution to journal › Article

*Quasigroups and Related Systems*, vol. 24, no. 1, pp. 103-108.

}

TY - JOUR

T1 - Steiner loops satisfying the statement of Moufang's theorem

AU - De Lourdes Merlini Giuliani, Maria

AU - Dos Anjos, Giliard Souza

AU - Colbourn, Charles

PY - 2016

Y1 - 2016

N2 - 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.

AB - 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.

KW - Moufang loop

KW - Moufang theorem

KW - Steiner loop

UR - http://www.scopus.com/inward/record.url?scp=84983371839&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84983371839&partnerID=8YFLogxK

M3 - Article

VL - 24

SP - 103

EP - 108

JO - Quasigroups and Related Systems

JF - Quasigroups and Related Systems

SN - 1561-2848

IS - 1

ER -