On product-one sequences over subsets of groups

Abstract

AbstractLet G be a group and $$G_0 \subseteq G$$ G 0 ⊆ G be a subset. A sequence over $$G_0$$ G 0 means a finite sequence of terms from $$G_0$$ 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 the infinite dihedral group.