On a “grouplike” family of quasigroups

Quasigroups are algebraic structures in which divisibility is always defined. This paper illustrates some similarities and differences between quasigroup theory and group theory, by singling out a special family of quasigroups which seem to be most “grouplike”. •We illustrate several similarities be...

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Bibliographic Details
Published inExamples and counterexamples Vol. 8; p. 100200
Main Authors Fares, Ahmed Al, Karaali, Gizem
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.12.2025
Elsevier
Subjects
Groups
Loops
Multiplication groups
Quasigroups
Quasigroups
Loops
Groups
Multiplication groups
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ISSN2666-657X
2666-657X
DOI10.1016/j.exco.2025.100200

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Summary:Quasigroups are algebraic structures in which divisibility is always defined. This paper illustrates some similarities and differences between quasigroup theory and group theory, by singling out a special family of quasigroups which seem to be most “grouplike”. •We illustrate several similarities between quasigroup theory and group theory.•We also illustrate a handful of differences between quasigroup theory and group theory.•We single out a special family of quasigroups which seem to be most “grouplike”.
ISSN:2666-657X
2666-657X
DOI:10.1016/j.exco.2025.100200