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arXiv · 2510.23543

The Erdős-Ginzburg-Ziv constant of rank-two-like $p$-groups

Benjamin Girard·Sofia Zotova
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Abstract

Adapting Reiher's proof of Kemnitz's conjecture, we obtain two refinements of a theorem of Schmid and Zhuang. Our main results provide improved upper bounds for the Erdős-Ginzburg-Ziv constant of rank-two-like $p$-groups, and their direct products with cyclic groups of order coprime to $p$. In particular, we determine the exact value of this constant, and also confirm a conjecture of Gao, for a new infinite family of groups of arbitrarily large rank.

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Benjamin Girard, Sofia Zotova. 2025-10-27. The Erdős-Ginzburg-Ziv constant of rank-two-like $p$-groups. https://arxiv.org/abs/2510.23543

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