The Cayley isomorphism property for groups of order 8p

TL;DR

This paper proves that certain groups of order 8p are DCI-groups, completing the classification of CI-groups of that order, which has implications for understanding symmetries in algebraic structures.

Contribution

It establishes that groups $Q imes Z_p$ and $Z_2^3 imes Z_p$ are DCI-groups for all primes p > 3, filling a gap in the classification of CI-groups of order 8p.

Findings

Q × Z_p and Z_2^3 × Z_p are DCI-groups for all primes p > 3

Complete classification of CI-groups of order 8p

Advances understanding of Cayley isomorphism properties in group theory

Abstract

For every prime $p>3$ we prove that $Q \times \mathbb{Z}_p$ and $\mathbb{Z}_2^3 \times \mathbb{Z}_p$ are DCI- groups. This result completes the description of CI-groups of order $8p$.