Abelian-by-Cyclic Moufang Loops

作者：Grishkov Alexander N; Zavarnitsine Andrei V^*

来源：Communications in Algebra, 2013, 41(6): 2242-2253.

DOI：10.1080/00927872.2012.655436

• Groups with triality
• Moufang loops
• 08A05
• 20E34
• 20N05

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 [<xref rid="CIT0010" ref-type="bibr">10</xref>] loops of this type of odd order 3q(3), with prime q1(mod3), are particular cases of our series. Some of the examples are shown to be embeddable into a Cayley algebra.

• 出版日期2013-5-21