Geodesic
$G$-Identities of Nilpotent Groups. I
Algebra i logika, Tome 40 (2001) no. 1, pp. 3-21

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The structure of a group $V_{n,red}(G)$ of reduced $G$-identities of rank $n$ is treated subject to the condition that $G$ is a nilpotent group of class 1 or 2. The results obtained allow us to settle the question of whether a $G$-variety $G$-$\operatorname{var}(G)$ generated by a nilpotent group $G$ of class 2 is finitely based. Moreover, we introduce the concepts of a $d$-commutator subgroup and of a main $d$-group, associated with $G$.
Keywords: a group of reduced $G$-identities, nilpotent group of class 2, $G$-variety, finitely based $G$-variety. 
@article{AL_2001_40_1_a0,
     author = {M. G. Amaglobeli},
     title = {$G${-Identities} of {Nilpotent} {Groups.~I}},
     journal = {Algebra i logika},
     pages = {3--21},
     publisher = {mathdoc},
     volume = {40},
     number = {1},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2001_40_1_a0/}
}
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M. G. Amaglobeli. $G$-Identities of Nilpotent Groups. I. Algebra i logika, Tome 40 (2001) no. 1, pp. 3-21. http://geodesic.mathdoc.fr/item/AL_2001_40_1_a0/