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arXiv · 1202.3228

Abelian-by-cyclic Moufang loops

Alexander N. Grishkov·Andrei V. Zavarnitsine
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Abstract

We use groups with triality to construct a series of nonassociative Moufang loops. Certain members of this series contain an abelian normal subloop with the corresponding quotient being a cyclic group. In particular, we give a new series of examples of finite abelian-by-cyclic Moufang loops. The previously known [A. Rajah, J. Alg., 235 (2001), 66-93] loops of this type of odd order 3q^3, with prime q congruent to 1 mod 3, are particular cases of our series. Some of the examples are shown to be embeddable into a Cayley algebra.

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Alexander N. Grishkov, Andrei V. Zavarnitsine. 2012-02-15. Abelian-by-cyclic Moufang loops. https://doi.org/10.1080/00927872.2012.655436

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