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On connected quandles of prime power order

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arxiv 1904.12801 v2 pith:BWLGYKOI submitted 2019-04-29 math.GR

Giuliano Bianco , Marco Bonatto This is my paper · ORCID
classification math.GR
keywords connectedquandlessizeloopspowerprimealgebraicautomorphic
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abstract

We develop some general ideas to study connected quandles of prime power size and we classify non-affine connected quandles of size $p^3$ for $p>3$, using a combination of group theoretical and universal algebraic tools. As a byproduct we obtain a classification of Bruck loops of the same size and that they are in one-to-one correspondence with commutative automorphic loops.

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  1. General constructions of biquandles and their symmetries

    math.GR 2019-08 conditional novelty 7.0 of 10

    All word pairs over two free generators that make every group a birack or biquandle are classified, and new union, product, holomorph, and covering constructions for biquandles are introduced with their automorphism groups.

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