Abstract
Let be a finite group. A finite unordered sequence of terms from , where repetition is allowed, is a product-one sequence if its terms can be ordered such that their product equals , the identity element of the group. As usual, we consider sequences as elements of the free abelian monoid with basis , and we study the submonoid of all product-one sequences. This is a finitely generated C-monoid, which is a Krull monoid if and only if is abelian. In case of abelian groups, is a well-studied object. In the present paper we focus on nonabelian groups, and we study the class semigroup and the arithmetic of .
Citation
Jun Seok Oh. "On the algebraic and arithmetic structure of the monoid of product-one sequences." J. Commut. Algebra 12 (3) 409 - 433, Fall 2020. https://doi.org/10.1216/jca.2020.12.409
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