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Pentagonal quasigroups, their translatability and parastrophes
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Journal Article
Pentagonal quasigroups, their translatability and parastrophes
2021
Overview
Any pentagonal quasigroup
is proved to have the product
, where
is an Abelian group,
is its regular automorphism satisfying
and
is the identity mapping. All Abelian groups of order
inducing pentagonal quasigroups are determined. The variety of commutative, idempotent, medial groupoids satisfying the pentagonal identity
is proved to be the variety of commutative, pentagonal quasigroups, whose spectrum is
. We prove that the only translatable commutative pentagonal quasigroup is
. The parastrophes of a pentagonal quasigroup are classified according to well-known types of idempotent translatable quasigroups. The translatability of a pentagonal quasigroup induced by the group
and its automorphism
is proved to determine the value of
and the range of values of
Publisher
De Gruyter,De Gruyter Brill Sp. z o.o., Paradigm Publishing Services
Subject
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