The Erdős-Ginzburg-Ziv constant of rank-two-like $p$-groups
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911234954100736 |
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| author | Girard, Benjamin Zotova, Sofia |
| author_facet | Girard, Benjamin Zotova, Sofia |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_23543 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Erdős-Ginzburg-Ziv constant of rank-two-like $p$-groups Girard, Benjamin Zotova, Sofia Combinatorics Group Theory Number Theory 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. |
| title | The Erdős-Ginzburg-Ziv constant of rank-two-like $p$-groups |
| topic | Combinatorics Group Theory Number Theory |
| url | https://arxiv.org/abs/2510.23543 |