Common transversals and complements in abelian groups
Group Theory
2025-02-21 v1
Abstract
Given a finite abelian group and cyclic subgroups , , of of the same order, we find necessary and sufficient conditions for , , to admit a common transversal for the cosets they afford. For an arbitrary number of cyclic subgroups we give a sufficient criterion when there exists a common complement. Moreover, in several cases where a common transversal exists, we provide concrete constructions.
Cite
@article{arxiv.2308.06559,
title = {Common transversals and complements in abelian groups},
author = {Stefanos Aivazidis and Maria Loukaki and Benjamin Sambale},
journal= {arXiv preprint arXiv:2308.06559},
year = {2025}
}
Comments
14 pages