论文标题
关于组的产品序列对组的子集
On product-one sequences over subsets of groups
论文作者
论文摘要
令$ g $为一个组，$ g_0 \ subseteq g $为子集。 $ g_0 $的序列是指$ g_0 $的有限术语序列，其中无视元素的顺序并允许重复元素。产品序列是一个序列，可以对其元素进行排序，以使其产品等于组的身份元素。我们研究了$ g $的有限亚集和整个组$ g $的一个序列序列的代数和算术特性，并特别强调了无限的二面基团。
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.
