On Relationship of Multiplication Groups and Isostrophic Quasigroups

Abstract

This study presented a kind of characterization of multiplication group of a quasi group , ∘ and of a loop (, ⋅) that are isostrophic, that is some parastrophes of quasigroup , ∘ with loops (,⋅). In particular, the middle multiplication groups of a quasi group (, ⋅) and of loops (, ∘) that are isostrophes (, ∘) were studied. Relationship of middle multiplication groups of a quasi group (, ⋅) to right(left) multiplication group of a loop , ∘ isostrophes were show to be coincided and their multiplication groups were show to be normal subgroups, using the concept of middle translation