TOPICS
Search

Quasigroup

A groupoid S such that for all a,b in S, there exist unique x,y in S such that

ax=b
(1)
ya=b.
(2)

No other restrictions are applied; thus a quasigroup need not have an identity element, not be associative, etc. Quasigroups are precisely groupoids whose multiplication tables are Latin squares. A quasigroup can be empty.

See also

Algebraic Loop, Binary Operator, Groupoid, Latin Square, Monoid, Semigroup

Explore with Wolfram|Alpha

References

Albert, A. A. (Ed.). Studies in Modern Algebra. Washington, DC: Math. Assoc. Amer., 1963.van Lint, J. H. and Wilson, R. M. A Course in Combinatorics. New York: Cambridge University Press, 1992.

Referenced on Wolfram|Alpha

Quasigroup

Cite this as:

Weisstein, Eric W. "Quasigroup." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Quasigroup.html

Subject classifications