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Two Galois connections for left quasigroups

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arxiv 2311.14574 v1 pith:L2AJZKLG submitted 2023-11-24 math.GR

Marco Bonatto This is my paper · ORCID
classification math.GR
keywords leftquasigroupscongruenceconnectionsgaloislatticequandlessubgroups
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We investigate two Galois connection between the congruence lattice and the lattice of subgroups of the displacement group of left quasigroups. Such connections were already studied for racks and quandles. We introduce the class of left quasigroups having congruence determined by subgroups (resp. orbits) and we extend a known result for quandles.

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  1. On Simply Connected Quandles

    math.GR 2025-04 conditional novelty 7.0 of 10

    A finite quandle is simply connected exactly when it is principal and all prime-size abelian cocycles are trivial, which yields classifications for sizes p^2 and p^3.

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