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

Edward Dobson¹

¹Mississippi State University and University of Primorska

The electronic journal of combinatorics, Tome 21 (2014) no. 3

Résumé

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 $p$).

Détail

DOI : 10.37236/3123

Classification : 05E18, 05C25, 20F18
Mots-clés : Cayley object, Cayley graph, isomorphism problem, CI-group