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Reference.org
Quasigroup
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<p>In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, especially in <a href="/facts/Abstract_algebra/YNNE1CNz">abstract algebra</a>, a quasigroup is an <a href="/facts/Algebraic_structure/TkuXca24">algebraic structure</a> that resembles a <a href="/facts/Group_(mathematics)/IQTYqINt">group</a> in the sense that "<a href="/facts/Division_(mathematics)/FqLKNkmq">division</a>" is always possible. Quasigroups differ from groups mainly in that the <a href="/facts/Associative/EQX8lV6r">associative</a> and <a href="/facts/Identity_element/9nss3xHY">identity element</a> properties are optional. In fact, a nonempty associative quasigroup is a group. </p><p>A quasigroup that has an identity element is called a loop. </p>