The paper studies the properties of n -ary Т-quasigroups (n 3). The isomorphism of the derived n -ary groups from two Т-groups for an n -ary Т-quasigroup is proved. A necessary and sufficient condition is found under which an n -ary loop is a derivative of an n -ary group from a Т-group for an n -ary Т-quasigroup. The coincidence of the class of n -ary T-quasigroups with the class of affine n -ary quasigroups is proved. The heredity, homomorphic and multiplicative closure of the class of all n -ary T-quasigroups are established, which means that this class is a variety.
N. A. Shchuchkin (Sun,) studied this question.