Crossed modules, Crossed n-fold extension of groups and Cohomology theory in Abstract Categories
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.
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 , the number of nilpotent loops of order up to isotopy, instead of isomorphy.