# On product-one sequences over dihedral groups

@article{Geroldinger2020OnPS, title={On product-one sequences over dihedral groups}, author={Alfred Geroldinger and David J. Grynkiewicz and Jun Seok Oh and Qinghai Zhong}, journal={Journal of Algebra and Its Applications}, year={2020} }

Let [Formula: see text] be a finite group. A sequence over [Formula: see text] means a finite sequence of terms from [Formula: see text], where repetition is allowed and the order is disregarded. A product-one sequence is a sequence whose elements can be ordered such that their product equals the identity element of the group. The set of all product-one sequences over [Formula: see text] (with the concatenation of sequences as the operation) is a finitely generated C-monoid. Product-one… Expand

#### 3 Citations

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Let $C_n$ be a cyclic group of order $n$. A sequence $S$ of length $\ell$ over $C_n$ is a sequence $S = a_1\boldsymbol\cdot a_2\boldsymbol\cdot \ldots\boldsymbol\cdot a_{\ell}$ of $\ell$ elements in… Expand

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Let G be a multiplicatively written finite group. We denote by E(G) the smallest integer t such that every sequence of t elements in G contains a product-one subsequence of length |G|. In 1961,… Expand

On product-one sequences over subsets of groups

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Let $G$ be a group and $G_0 \subseteq G$ be a subset. A sequence over $G_0$ means a finite sequence of terms from $G_0$, where the order of elements is disregarded and the repetition of elements is… Expand

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