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A dense family of well-behaved finite monogenerated left-distributive groupoids

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Abstract

We construct a family \(\fancyscript{F}\), indexed by five integer parameters, of finite monogenerated left-distributive (LD) groupoids with the property that every finite monogenerated LD groupoid is a quotient of a member of \(\fancyscript{F}\). The combinatorial abundance of finite monogenerated LD groupoids is encoded in the congruence lattices of the groupoids \(\fancyscript{F}\), which we show to be extremely large.

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Authors and Affiliations

  1. Department of Mathematics, Vanderbilt University, 1227 Stevenson Center, Nashville, TN, 37240, USA

    Matthew Smedberg

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  1. Matthew Smedberg
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Correspondence to Matthew Smedberg.

Additional information

Portions of the research for this paper were completed on a fellowship at the Fields Institute, Toronto, ON, Canada.

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Smedberg, M. A dense family of well-behaved finite monogenerated left-distributive groupoids. Arch. Math. Logic 52, 377–402 (2013). https://doi.org/10.1007/s00153-012-0320-9

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  • DOI: https://doi.org/10.1007/s00153-012-0320-9

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