English

Abelian-by-cyclic Moufang loops

Group Theory 2013-05-16 v1

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.

Keywords

Cite

@article{arxiv.1202.3228,
  title  = {Abelian-by-cyclic Moufang loops},
  author = {Alexander N. Grishkov and Andrei V. Zavarnitsine},
  journal= {arXiv preprint arXiv:1202.3228},
  year   = {2013}
}

Comments

Preprint submitted to Comm. Alg

R2 v1 2026-06-21T20:19:36.687Z