  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.
