A Note on Sumsets and Difference Sets in Groups of Order 12

Resumo

A subset $A$ of a group $G$ is referred to as a balanced set when $|A+A|=|A-A|$, MSTD (more sums than differences) when $|A+A|>|A-A|$, and MDTS (more differences than sums) when $|A-A|>|A+A|$. In this paper, we present a comparative study of MSTD and MDTS sets in groups of order 12 up to isomorphism. Additionally, we have completely categorized such sets in these groups and have provided a set $A$ with the current highest value of $ln(|A+A|)/ln(|A-A|).$