Near-factorizations of dihedral groups

TL;DR

This paper explores near-factorizations in dihedral groups, showing equivalences among known constructions, providing new examples via computational methods, and analyzing a specific construction method from cyclic groups.

Contribution

It identifies when near-factorizations in dihedral groups are equivalent or distinct, introduces new examples, and analyzes a construction method from cyclic groups.

Findings

Few known nonequivalent near-factorizations in dihedral groups

New examples of near-factorizations found using computational tools

Analysis of Pêcher's construction method for near-factorizations

Abstract

We investigate near-factorizations of nonabelian groups, concentrating on dihedral groups. We show that some known constructions of near-factorizations in dihedral groups yield equivalent near-factorizations. In fact, there are very few known examples of nonequivalent near-factorizations in dihedral or other nonabelian groups; we provide some new examples with the aid of the computer. We also analyse a construction for near-factorizations in dihedral groups from near-factorizations in cyclic groups, due to P\^{e}cher, and we investigate when nonequivalent near-factorizations can be obtained by this method.