quasigroup

Noun

Meaning

English Wikipedia has an article on:quasigroupWikipedia
quasigroup (plural quasigroups)

(mathematics) An algebraic structure, resembling a group, whose arithmetic may not be associative

Examples

Conversely, every Latin square can be taken as the multiplication table of a quasigroup in many ways: the border row (containing the column headers) and the border column (containing the row headers) can each be any permutation of the elements. Source: Internet

A quasigroup homotopy from Q to P is a triple (α, β, γ) of maps from Q to P such that : for all x, y in Q. A quasigroup homomorphism is just a homotopy for which the three maps are equal. Source: Internet

A magma Q is a quasigroup precisely when all these operators, for every x in Q, are bijective. Source: Internet

Every quasigroup is isotopic to a loop. Source: Internet

Conjugation (parastrophe) Left and right division are examples of forming a quasigroup by permuting the variables in the defining equation. Source: Internet

Conversely, any (finite) quasigroup with these properties arises from a Steiner triple system. Source: Internet

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