ON MULTIPLICATION GROUPS OF ISOSTROPHIC QUASIGROUPS

Ion GRECU Moldova State University

Abstract

A loop is called a middle Bol loop if every loop isotope of satisfies the identity (i.e. if the anti-autmorphic inverse property is universal in ). Middle Bol loops are isostrophes of left (right) Bol loops. Multiplication groups of a quasigroup and of loops which are isostrophic to are characterized. In particular, it is proved that the right multiplication group of a middle Bol loop coincides with the left (right) multiplication group of the corresponding right (left) Bol loop. Some properties of the stabilizer of an element in the right (left) multiplication group of isostrophic quasigroups are established. Keywords: Bol loop, middle Bol loop, isostrophy, universal properties, multiplication groups, stabilizer.