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Quasigroups arisen by right nuclear extension

Péter T. Nagy; Izabella Stuhl — 2012

Commentationes Mathematicae Universitatis Carolinae

The aim of this paper is to prove that a quasigroup $Q$ with right unit is isomorphic to an $f$ -extension of a right nuclear normal subgroup $G$ by the factor quasigroup $Q / G$ if and only if there exists a normalized left transversal $Σ \subset Q$ to $G$ in $Q$ such that the right translations by elements of $Σ$ commute with all right translations by elements of the subgroup $G$ . Moreover, a loop $Q$ is isomorphic to an $f$ -extension of a right nuclear normal subgroup $G$ by a loop if and only if $G$ is middle-nuclear, and there exists...

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