Geodesic
$G$-Identities of Nilpotent Groups.~II
Algebra i logika, Tome 40 (2001) no. 4, pp. 377-395.

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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. 
@article{AL_2001_40_4_a1,
     author = {M. G. Amaglobeli},
     title = {$G${-Identities} of {Nilpotent} {Groups.~II}},
     journal = {Algebra i logika},
     pages = {377--395},
     publisher = {mathdoc},
     volume = {40},
     number = {4},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2001_40_4_a1/}
}
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M. G. Amaglobeli. $G$-Identities of Nilpotent Groups.~II. Algebra i logika, Tome 40 (2001) no. 4, pp. 377-395. http://geodesic.mathdoc.fr/item/AL_2001_40_4_a1/