Displaying similar documents to “On Mikheev's construction of enveloping groups”

Groups, transversals, and loops

Tuval Foguel (2000)

Commentationes Mathematicae Universitatis Carolinae

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A family of loops is studied, which arises with its binary operation in a natural way from some transversals possessing a ``normality condition''.

A scoop from groups: equational foundations for loops

Phillips, J. D., Petr Vojtěchovský (2008)

Commentationes Mathematicae Universitatis Carolinae

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Groups are usually axiomatized as algebras with an associative binary operation, a two-sided neutral element, and with two-sided inverses. We show in this note that the same simplicity of axioms can be achieved for some of the most important varieties of loops. In particular, we investigate loops of Bol-Moufang type in the underlying variety of magmas with two-sided inverses, and obtain ``group-like'' equational bases for Moufang, Bol and C-loops. We also discuss the case when the inverses...

Relatives of K-loops: Theory and examples

Hubert Kiechle (2000)

Commentationes Mathematicae Universitatis Carolinae

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A or is a Bol loop with the automorphic inverse property. An overview of the most important theorems on K-loops and some of their relatives, especially Kikkawa loops, is given. First, left power alternative loops are discussed, then Kikkawa loops are considered. In particular, their nuclei are determined. Then the attention is paid to general K-loops and some special classes of K-loops such as 2-divisible ones. To construct examples, the method of is introduced. This has been used...