On the Cayley isomorphism problem for Cayley objects of nilpotent groups of some orders (Q405288)

Summary: We give a necessary condition to reduce the Cayley isomorphism problem for Cayley objects of a nilpotent or abelian group \(G\) whose order satisfies certain arithmetic properties to the Cayley isomorphism problem of Cayley objects of the Sylow subgroups of \(G\) in the case of nilpotent groups, and in the case of abelian groups to certain natural subgroups. As an application of this result, we show that \({\mathbb Z}_q\times{\mathbb Z}_p^2\times{\mathbb Z}_m\) is a CI-group with respect to digraphs, where \(q\) and \(p\) are primes with \(p^2 q\) and \(m\) is a square-free integer satisfying certain arithmetic conditions (but there are no other restrictions on \(q\) and \(p\)).