Geodesic
A Levi class generated by a quasivariety of nilpotent groups
Algebra i logika, Tome 58 (2019) no. 4, pp. 486-499

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Let $L(M)$ be a class of all groups $G$ in which the normal closure of any element belongs to $M$; $qM$ is a quasivariety generated by a class $M$. We consider a quasivariety $qH_2$ generated by a relatively free group in a class of nilpotent groups of class at most $2$ with commutator subgroup of exponent $2$. It is proved that the Levi class $L(qH_2)$ generated by the quasivariety $qH_2$ is contained in the variety of nilpotent groups of class at most $3$.
Mots-clés : group
Keywords: nilpotent group, variety, quasivariety, Levi class. 
@article{AL_2019_58_4_a4,
     author = {V. V. Lodeishchikova},
     title = {A {Levi} class generated by a quasivariety of nilpotent groups},
     journal = {Algebra i logika},
     pages = {486--499},
     publisher = {mathdoc},
     volume = {58},
     number = {4},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2019_58_4_a4/}
}
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V. V. Lodeishchikova. A Levi class generated by a quasivariety of nilpotent groups. Algebra i logika, Tome 58 (2019) no. 4, pp. 486-499. http://geodesic.mathdoc.fr/item/AL_2019_58_4_a4/