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arXiv · 1610.09870

Extremal product-one free sequences in $C_q \rtimes_s C_m$

Fabio Enrique Brochero Martínez·Sávio Ribas
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Abstract

Let $G$ be a finite group, written multiplicatively. The Davenport constant of $G$ is the smallest positive integer $d$ such that every sequence of $G$ with $d$ elements has a non-empty subsequence with product $1$. Let $C_n \simeq \mathbb Z_n$ be the cyclic group of order $n$. Bass (2007) showed that the Davenport constant of the metacyclic group $C_q \rtimes_s C_m$, where $q$ is a prime number and $\text{ord}_q(s) = m \ge 2$, is $m+q-1$. In this paper, we explicit the form of all sequences $S$ of $C_q \rtimes_s C_m$, with $q+m-2$ elements, that are free of product-$1$ subsequences.

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Fabio Enrique Brochero Martínez, Sávio Ribas. 2016-10-31. Extremal product-one free sequences in $C_q \rtimes_s C_m$. https://arxiv.org/abs/1610.09870

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