Let G be a finite group. A sequence over G means a finite sequence of terms from G, 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 G (with the concatenation of sequences as the operation) is a finitely generated C-monoid. Product-one sequences over dihedral groups have a variety of extremal properties. This paper provides a detailed investigation, with methods from arithmetic combinatorics, of the arithmetic of the monoid of product-one sequences over dihedral groups.

中文翻译：

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关于二面体群上的产品一序列

让G是一个有限群。一个序列结束G表示来自的有限项序列G, 允许重复并且忽略顺序。product-one 序列是一个序列，其元素可以排序，使得它们的乘积等于组的标识元素。所有product-one序列的集合G（以序列的串联作为操作）是一个有限生成的 C-monoid。二面体群上的积一序列具有多种极值性质。本文使用算术组合学的方法对二面体群上的积一序列的幺半群的算术进行了详细的研究。