On the distance between non-isomorphic groups

TL;DR

This paper explores the minimal differences between the multiplication tables of non-isomorphic groups, establishing bounds based on group homomorphism testing results.

Contribution

It provides a tight lower bound on the distance between multiplication tables of non-isomorphic groups using homomorphism testing techniques.

Findings

Established a lower bound on the distance between non-isomorphic groups' tables.

Connected group testing results to structural differences in groups.

Extended understanding of group isomorphism testing complexity.

Abstract

A result of Ben-Or, Coppersmith, Luby and Rubinfeld on testing whether a map be two groups is close to a homomorphism implies a tight lower bound on the distance between the multiplication tables of two non-isomorphic groups.