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Varieties of quasigroups arising from 2-perfect m-cycle systems

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Abstract

For m = 6 and for all odd composite integers m, as well as for all even integers m ≥ 10 that satisfy certain conditions, 2-perfect m-cycle systems are constructed whose quasigroups have a homomorphism onto quasigroups which do not correspond to a 2-perfect m-cycle systems. Thus it is shown that for these values of m the class of quasigroups arising from all 2-perfect m-cycle systems does not form a variety.

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Authors and Affiliations

  1. Department of Mathematics, The University of Queensland, 4072, QLD, Australia

    Darryn E. Bryant

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  1. Darryn E. Bryant
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Communicated by D. Jungnickel

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Bryant, D.E. Varieties of quasigroups arising from 2-perfect m-cycle systems. Des Codes Crypt 2, 159–168 (1992). https://doi.org/10.1007/BF00124894

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  • DOI: https://doi.org/10.1007/BF00124894

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