Editing Quasigroup (section)

{{Short description|Magma obeying the Latin square property}}
[[File:Magma to group4.svg|thumb|right|300px|Algebraic structures between [[Magma (algebra)|magmas]] and [[Group (mathematics)|groups]]: A ''quasigroup'' is a [[magma (algebra)|magma]] with the type of [[Division (mathematics)#Abstract algebra|divisibility]] given by the [[Quasigroup#Algebra|Latin square property]]. A [[Quasigroup#Loops|loop]] is a ''quasigroup'' with an [[identity element]].]]{{No footnotes|date=February 2024}}
In [[mathematics]], especially in [[abstract algebra]], a '''quasigroup''' is an [[algebraic structure]] that resembles a [[group (mathematics)|group]] in the sense that "[[division (mathematics)|division]]" is always possible. Quasigroups differ from groups mainly in that the [[associative]] and [[identity element]] properties are optional. In fact, a nonempty associative quasigroup is a group.<ref>[https://groupprops.subwiki.org/wiki/Nonempty_associative_quasigroup_equals_group Nonempty associative quasigroup equals group]</ref><ref>[https://planetmath.org/anassociativequasigroupisagroup an associative quasigroup is a group]</ref>

A quasigroup that has an identity element is called a '''loop'''.

{{Algebraic structures |Group}}