On product-one sequences over dihedral groups
Number Theory
2020-11-17 v2 Commutative Algebra
Combinatorics
Group Theory
Abstract
Let be a finite group. A sequence over means a finite sequence of terms from , 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 (with 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 article provides a detailed investigation, with methods from arithmetic combinatorics, of the arithmetic of the monoid of product-one sequences over dihedral groups.
Cite
@article{arxiv.1910.12484,
title = {On product-one sequences over dihedral groups},
author = {Alfred Geroldinger and David J. Grynkiewicz and Jun Seok Oh and Qinghai Zhong},
journal= {arXiv preprint arXiv:1910.12484},
year = {2020}
}
Comments
to appear in Journal of Algebra and its Applications