Common transversals and complements in abelian groups
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866910836067401728 |
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| author | Aivazidis, Stefanos Loukaki, Maria Sambale, Benjamin |
| author_facet | Aivazidis, Stefanos Loukaki, Maria Sambale, Benjamin |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_06559 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Common transversals and complements in abelian groups Aivazidis, Stefanos Loukaki, Maria Sambale, Benjamin Group Theory 05D15, 05E16, 20D60 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. |
| title | Common transversals and complements in abelian groups |
| topic | Group Theory 05D15, 05E16, 20D60 |
| url | https://arxiv.org/abs/2308.06559 |