• Corpus ID: 245986468

# On the direct and inverse zero-sum problems over \$C_n \rtimes_s C_2\$

```@inproceedings{Avelar2022OnTD,
title={On the direct and inverse zero-sum problems over \\$C\_n \rtimes\_s C\_2\\$},
author={Danilo Vilela Avelar and Fabio Enrique Brochero Mart'inez and S{\'a}vio Ribas},
year={2022}
}```
• Published 14 January 2022
• Mathematics
Let Cn be the cyclic group of order n. In this paper, we provide the exact values of some zero-sum constants over Cn⋊sC2 where s 6≡ ±1 (mod n), namely η-constant, Gao constant, and ErdősGinzburg-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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