(Institutul de Matematică şi Informatică al AŞM, 2020) Syrbu, Parascovia; Grecu, Ion
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.
