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Crossed product of cyclic groups

Ana-Loredana Agore, Dragoş Frățilă (2010)

Czechoslovak Mathematical Journal

All crossed products of two cyclic groups are explicitly described using generators and relations. A necessary and sufficient condition for an extension of a group by a group to be a cyclic group is given.

Enumeration of nilpotent loops up to isotopy

Lucien Clavier (2012)

Commentationes Mathematicae Universitatis Carolinae

We modify tools introduced in [Daly D., Vojtěchovský P., Enumeration of nilpotent loops via cohomology, J. Algebra 322 (2009), no. 11, 4080–4098] to count, for any odd prime q , the number of nilpotent loops of order 2 q up to isotopy, instead of isomorphy.

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