Polyadic $\mathrm{Т}$-quasigroups

The paper studies the properties of $n$-ary $\mathrm{Т}$-quasigroups ($n\geq3$). The isomorphism of the derived $n$-ary groups from two $\mathrm{Т}$-groups for an $n$-ary $\mathrm{Т}$-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 $\mathrm{Т}$-group for an $n$-ary $\mathrm{Т}$-quasigroup. The coincidence of the class of $n$-ary $\mathrm{Т}$ quasigroups with the class of affine $n$-ary quasigroups is proved. The heredity, homomorphic and multiplicative closure of the class of all $n$-ary $\mathrm{Т}$-quasigroups are established, which means that this class is a variety.