Displaying similar documents to “ G - n -quasigroups.”

Algebraic aspects of web geometry

Maks A. Akivis, Vladislav V. Goldberg (2000)

Commentationes Mathematicae Universitatis Carolinae

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Algebraic aspects of web geometry, namely its connections with the quasigroup and loop theory, the theory of local differential quasigroups and loops, and the theory of local algebras are discussed.

A class of quasigroups solving a problem of ergodic theory

Jonathan D. H. Smith (2000)

Commentationes Mathematicae Universitatis Carolinae

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A pointed quasigroup is said to be semicentral if it is principally isotopic to a group via a permutation on one side and a group automorphism on the other. Convex combinations of permutation matrices given by the one-sided multiplications in a semicentral quasigroup then yield doubly stochastic transition matrices of finite Markov chains in which the entropic behaviour at any time is independent of the initial state.

When is it hard to show that a quasigroup is a loop?

Anthony Donald Keedwell (2008)

Commentationes Mathematicae Universitatis Carolinae

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We contrast the simple proof that a quasigroup which satisfies the Moufang identity ( x · y z ) x = x y · z x is necessarily a loop (Moufang loop) with the remarkably involved prof that a quasigroup which satisfies the Moufang identity ( x y · z ) y = x ( y · z y ) is likewise necessarily a Moufang loop and attempt to explain why the proofs are so different in complexity.