The Cayley isomorphism property for the group C^5_2\times C_p

Grigory Ryabov

Abstract


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 C25 × Cp, where p is a prime, is a DCI-group if and only if p ≠ 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 ≠ 2 and G ≅ C25 × Cp.


Keywords


Isomorphisms, DCI-groups, Schur rings.

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DOI: https://doi.org/10.26493/1855-3974.2348.f42

ISSN: 1855-3974

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