On the direct and inverse zero-sum problems over Cn ⋊s C2.
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2022
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Let Cn be the cyclic group of order n. In this paper, we provide the exact values of some
zero-sum constants over Cn ⋊s C2 where s 6≡ ±1 (mod n), namely η-constant, Gao constant, and Erdős-
Ginzburg-Ziv constant (the latter for all but a “small” family of cases). As a consequence, we prove
the Gao’s and Zhuang-Gao’s Conjectures for groups of this form. We also solve the associated inverse
problems by characterizing the structure of product-one free sequences over Cn ⋊s C2 of maximum
length.
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AVELAR, D. V.; BROCHERO MARTINEZ, F. E.; RIBAS, S. On the direct and inverse zero-sum problems over Cn ⋊s C2. Journal of Combinatorial Theory Series A, v. 197, artigo 105751, 2023. Disponível em: <https://www.sciencedirect.com/science/article/pii/S0097316523000195>. Acesso em: 06 jul. 2023.