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 ofloops which areisostrophic to are haracterized. 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 sostrophic quasigroups are established.
