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) |
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Pages (from-to) | 103-108 |
Number of pages | 6 |
Journal | Quasigroups and Related Systems |
Volume | 24 |
Issue number | 1 |
State | Published - 2016 |
Keywords
- Moufang loop
- Moufang theorem
- Steiner loop
ASJC Scopus subject areas
- Algebra and Number Theory
- Discrete Mathematics and Combinatorics