On product-one sequences over subsets of groups
On product-one sequences over subsets of groups
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DOI：
10.1007/s10998-022-00483-5
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发表时间：
2020-12
影响因子：
0.8
通讯作者：
Victor Fadinger;Qinghai Zhong
中科院分区：
文献类型：
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作者：
Victor Fadinger;Qinghai Zhong
设G是一个群，G是一个子集.一个序列是指一个有限的序列，其中元素的顺序被忽略，元素的重复是允许的。积一序列是一个序列，它的元素可以被排序，使得它们的乘积等于群的单位元素。本文研究了G的有限子集上和整个群G上的积一序列的幺半群的代数和算术性质，特别强调了无限二面体群。
LetGbe a group andbe a subset. A sequence overmeans a finite sequence of terms from, 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 ofGand over the whole groupG, with a special emphasis on the infinite dihedral group.