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Distributive Gruppen endlicher Ordnung [Finite Distributive Groups]

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arxiv 1403.6326 v2 pith:QHZJZ3ME submitted 2014-03-25 math.GR math.HO

classification math.GRmath.HO
keywords distributivegroupsbeforedefineleftrightaddedaddenda
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abstract

This is a translation. I have added translations for (possibly) outdated definitions in an appendix at the end. In this paper, we define distributive groups and show some properties of them. We then concern ourselves with the homogeinity of distributive groups, before showing how they can be generated from both associative and distributive groups. After that, we look at subgroups and define an index theorem for distributive groups before describing the structure of distributive groups. Finally, we present two addenda with several theorems that we proved while trying to prove that $\left|(A.p).(A.q)\right|=\left|A\right|$.

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  1. Path to homology of Yang-Baxter operators

    math.GT 2026-07 accept novelty 5.5 of 10

    A historical and personal survey of the path from knot theory and distributive homology to Yang-Baxter homology, including new homology computations for HOMFLYPT operators and a cubic face-map decomposition of the Rei...

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