Jun Seok Oh. Source: Journal of Commutative Algebra, Volume 12, Number 3, 409--433.Abstract:
Let [math] be a finite group. A finite unordered sequence [math] of terms from [math] , where repetition is allowed, is a product-one sequence if its terms can be ordered such that their product equals [math] , the identity element of the group. As usual, we consider sequences as elements of the free abelian monoid [math] with basis [math] , and we study the submonoid [math] of all product-one sequences. This is a finitely generated C-monoid, which is a Krull monoid if and only if [math] is abelian. In case of abelian groups, [math] is a well-studied object. In the present paper we focus on nonabelian groups, and we study the class semigroup and the arithmetic of [math] .