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P -hypergoupes

Thomas N. Vougiouklis, L. Konguetsof (1987)

Acta Universitatis Carolinae. Mathematica et Physica

Plenary stable quasigroups

Philip Holgate (1991)

Commentationes Mathematicae Universitatis Carolinae

Some results are obtained for quasigroups in which the operation of iterated squaring always leads to stability irrespective of the initial element.

Polyabelian loops and Boolean completeness

François Lemieux, Cristopher Moore, Denis Thérien (2000)

Commentationes Mathematicae Universitatis Carolinae

We consider the question of which loops are capable of expressing arbitrary Boolean functions through expressions of constants and variables. We call this property Boolean completeness. 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 polyabelian if it is an iterated affine quasidirect product of Abelian groups; polyabelianness...

Possible orders of nonassociative Moufang loops

Orin Chein, Andrew Rajah (2000)

Commentationes Mathematicae Universitatis Carolinae

The paper surveys the known results concerning the question: “For what values of n does there exist a nonassociative Moufang loop of order n ?” Proofs of the newest results for n odd, and a complete resolution of the case n even are also presented.

Powers and alternative laws

Nicholas Ormes, Petr Vojtěchovský (2007)

Commentationes Mathematicae Universitatis Carolinae

A groupoid is alternative if it satisfies the alternative laws x ( x y ) = ( x x ) y and x ( y y ) = ( x y ) y . These laws induce four partial maps on + × + ( r , s ) ...

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