Dihedral groups of order 2pq or 2pqr are DCI

2023/11/21 by Joy Morris, Morris, Joy
Mathematics · #05C25 #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research

paper · pdf · doi:10.48550/arxiv.2311.12277

openalex publication_date 2023/11/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A group has the (D)CI ((Directed) Cayley Isomorphism) property, or more commonly is a (D)CI group, if any two Cayley (di)graphs on the group are isomorphic via a group automorphism. That is, G is a (D)CI group if whenever \rmCay(G,S)≅ \rmCay(G,T), there is some δ∈ \rmAut(G) such that S^δ=T. (For the CI property, we only require this to be true if S and T are closed under inversion.) Suppose p,q,r are distinct odd primes. We show that D_2pqr is a DCI group. We present this result in the more general context of dihedral groups of squarefree order; some of our results apply to any such group, and may be useful in future toward showing that all dihedral groups of squarefree order are DCI groups.

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