LOOPS WITH INVARIANT FLEXIBILITY UNDER THE ISOSTROPHY

Abstract

The question ”Are the loops with universal (i.e. invariant under the isotopy of loops) flexibility law xy·x=x·yx , middle Bol loops?” is open in the theory of loops. If this conjecture is true then the loops for which a ll isostrophic loops are flexible are Moufang loops. In the present paper we prove that commutative loops with invariant flexibility under the isostrophy of loops are Mouf ang loops. In particular,we obtain that commutative IP -loops with universal flexibility are Moufang loops.