Common transversals and complements in abelian groups

authored by

S. Aivazidis, M. Loukaki, B. Sambale

Abstract

Given a finite abelian group G and cyclic subgroups A, B, C of G of the same order, we find necessary and sufficient conditions for A, B, C 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.

Organisation(s)

Institute of Algebra, Number Theory and Discrete Mathematics

External Organisation(s)

University of Crete

Type

Article

Journal

Journal of algebraic combinatorics

Volume

59

Pages

581-595

No. of pages

15

ISSN

0925-9899

Publication date

05.2024

Publication status

Published

Peer reviewed

Yes

ASJC Scopus subject areas

Algebra and Number Theory, Discrete Mathematics and Combinatorics

Electronic version(s)

https://doi.org/10.48550/arXiv.2308.06559 (Access: Open)
https://doi.org/10.1007/s10801-024-01299-x (Access: Open)