Abstract:
The structure of a group $V_{n,red}(G)$ of reduced $G$-identities is described subject to the condition that $G$ is a nilpotent group of class 3. We prove the criterion for a $G$-variety $G\operatorname{-var}(G)$ to be finitely based for such $G$.
Keywords:group of reduced $G$-identities, nilpotent group of class $3$, $G$-variety, finitely based variety.