The Cayley isomorphism property for the group Csub2sup5timesCsubp - Ryabov, Grigory (Ars mathematica contemporanea, 2020)
A finite group ?$G$? is called a DCI-group if two Cayley digraphs over ?$G$? are isomorphic if and only if their connection sets are conjugate by a group automorphism. We prove that the group ?$C_2^5 × C_p$?, where ?$p$? is a prime, is a DCI-group if and only if ?$p \ne 2$?. Together with the previously obtained results, this implies that a group ?$G$? of order ?$32p$?, where ?$p$? is a prime, is a DCI-group if and only if ?$p \ne 2$? and ?$G \cong C_2^5 × C_p$?.
Keywords: DCI-groups; DCI-grupa; isomorphisms; izomorfizmi; Schur rings; Schurovi kolobarji