Displaying similar documents to “On Steiner loops and power associativity.”

Polyabelian loops and Boolean completeness

François Lemieux, Cristopher Moore, Denis Thérien (2000)

Commentationes Mathematicae Universitatis Carolinae

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We consider the question of which loops are capable of expressing arbitrary Boolean functions through expressions of constants and variables. We call this property . It is a generalization of functional completeness, and is intimately connected to the computational complexity of various questions about expressions, circuits, and equations defined over the loop. We say that a loop is if it is an iterated affine quasidirect product of Abelian groups; polyabelianness coincides with solvability...

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.

Bol loops with a large left nucleus

Orin Chein, Edgar G. Goodaire (2008)

Commentationes Mathematicae Universitatis Carolinae

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Possession of a unique nonidentity commutator/associator is a property which dominates the theory of loops whose loop rings, while not associative, nevertheless satisfy an ``interesting'' identity. Indeed, until now, with the exception of some ad hoc examples, the only known class of Bol loops whose loop rings satisfy the right Bol identity have this property. In this paper, we identify another class of loops whose loop rings are ``strongly right alternative'' and present various constructions...