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arXiv · 2308.06559

Common transversals and complements in abelian groups

Stefanos Aivazidis·Maria Loukaki·Benjamin Sambale
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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.

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Stefanos Aivazidis, Maria Loukaki, Benjamin Sambale. 2023-08-12. Common transversals and complements in abelian groups. https://doi.org/10.1007/s10801-024-01299-x

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