Extending zero-sum theory from abelian to non-abelian groups

Abstract: Zero-sum theory is a central topic in additive combinatorics that studies the structure of sequences over finite groups and the conditions guaranteeing the existence of zero-sum subsequences. Fundamental parameters in this area include the Davenport constant and the Erdős–Ginzburg–Ziv constant, which measure the threshold lengths forcing zero-sum behavior. These invariants originated in the study of non-unique factorizations in algebraic number theory, but determining their exact values remains a challenging problem even for many finite abelian groups. In this talk, I will discuss recent progress on zero-sum problems in finite non-abelian groups. In particular, I will highlight how combinatorial techniques developed for abelian groups can be adapted—or fail—to extend to the non-abelian setting, and how new phenomena arise due to the lack of commutativity. I will also present several results that reveal surprising connections between classical zero-sum invariants of abelian groups and their analogues for non-abelian groups, pointing toward a broader combinatorial framework for zero-sum theory.

number theory

Audience: researchers in the topic

Combinatorial and additive number theory seminar (CANT 2026)