English

Common transversals and complements in abelian groups

Group Theory 2025-02-21 v1

Abstract

Given a finite abelian group GG and cyclic subgroups AA, BB, CC of GG of the same order, we find necessary and sufficient conditions for AA, BB, CC 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.

Keywords

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

R2 v1 2026-06-28T11:54:17.768Z