On product-one sequences over subsets of groups

Victor Fadinger; Qinghai Zhong

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arXiv · 2012.04600

On product-one sequences over subsets of groups

Victor Fadinger·Qinghai Zhong

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Abstract

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 allowed. A product-one sequence is a sequence whose elements can be ordered such that their product equals the identity element of the group. We study algebraic and arithmetic properties of monoids of product-one sequences over finite subsets of $G$ and over the whole group $G$, with a special emphasis on infinite dihedral groups.

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Victor Fadinger, Qinghai Zhong. 2020-12-01. On product-one sequences over subsets of groups. https://arxiv.org/abs/2012.04600

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