On product-one sequences over dihedral groups
Let G be a finite group. A sequence over G means a finite sequence of terms from G, where repetition is allowed and the order is disregarded. A product-one sequence is a sequence whose elements can be ordered such that their product equals the identity element of the group. The set of all product-one sequences over G (with the concatenation of sequences as the operation) is a finitely generated C-monoid. Product-one sequences over dihedral groups have a variety of extremal properties. This paper provides a detailed investigation, with methods from arithmetic combinatorics, of the arithmetic of the monoid of product-one sequences over dihedral groups.
Journal of Algebra and its Applications
Geroldinger, A., Grynkiewicz, D., Oh, J., & Zhong, Q. (2021). On product-one sequences over dihedral groups. Journal of Algebra and its Applications https://doi.org/10.1142/S0219498822500645