On autotopies of quasigroups

We consider the scheme of a quasigroup and prove in Theorem 1 that it is an invariant of the isotopy class of the quasigroup. The scheme of a quasigroup makes it possible in some cases to easily differentiate between nonisotopic quasigroups. We introduce the notions of autotopy of the first kind and of action of an autotopy on elements of a quasigroup. The nonexistence of a quasigroup of order $(4m+2)$ with a transitively acting group of autotopies of the first kind is proved (Theorem 3).