On product-one sequences over subsets of groups

2020/12/01 by Victor Fadinger, Fadinger, Victor, Qinghai Zhong +1 · 1 citation
Computer Science · Mathematics · #11B30 #13A50 #20M12 #20M13 #Coding theory and cryptography #FOS: Mathematics #Group Theory (math.GR) #Rings, Modules, and Algebras #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.2012.04600

openalex publication_date 2020/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a group and G₀ ⊆ G be a subset. A sequence over G₀ means a finite sequence of terms from G₀, 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.

Cited by

• The catenary degree of monoids of product-one sequences

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