# Elementary abelian groups of rank 5 are DCI-groups

## TL;DR

This paper proves that elementary abelian groups of rank 5 are DCI-groups, meaning their Cayley digraphs are isomorphic only when their connection sets are related by an automorphism, for any odd prime p.

## Contribution

It establishes that elementary abelian groups of rank 5 are DCI-groups for all odd primes, extending the class of known DCI-groups.

## Key findings

- Elementary abelian groups of rank 5 are DCI-groups.
- Cayley digraphs are isomorphic iff their connection sets are related by an automorphism.
- Valid for all odd primes p.

## Abstract

In this paper, we show that the group $\mathbb{Z}_p^5$ is a DCI-group for any odd prime $p,$ that is, two Cayley digraphs Cay$(\mathbb{Z}_p^5,S)$ and Cay$(\mathbb{Z}_p^5,T)$ are isomorphic if and only if $S=T^\varphi$ for some automorphism $\varphi$ of the group $\mathbb{Z}_p^5$.