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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 [Citation10] loops of this type of odd order 3q 3, with prime q ≡ 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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ACKNOWLEDGEMENT
Supported by FAPESP, Brazil (proc. 2010/51793-2); by the Russian Foundation for Basic Research (projects 12-01-90006, 11-01-91158) by the Council of the President grants (project NSc–3669.2010.1) by the Russian Federal Program “Scientific and pedagogic people of the innovative Russia” (contract 14.740.11.0346).
Notes
Communicated by I. Shestakov.