Polyadic T-quasigroups

The paper studies the properties of n-ary T-quasigroups ($n\geq3$). The isomorphism of the derived n-ary groups from two T-groups for an n-ary T-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 T-group for an n-ary T-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.