Geodesic
Absolutely Closed Groups in the Class of $2$-Step Nilpotent Torsion-Free Groups
Matematičeskie zametki, Tome 97 (2015) no. 6, pp. 936-941

Voir la notice de l'article provenant de la source Math-Net.Ru

It is proved that divisible groups and only these groups are absolutely closed (with respect to the operator of dominion) in the class of $2$-step nilpotent torsion-free groups. It is established that the additive group of the rationals is $1$-closed in an arbitrary quasivariety of nilpotent torsion-free groups and $3$-closed in an arbitrary quasivariety of $2$-step nilpotent torsion-free groups.
Keywords: quasivariety, dominion, absolutely closed group, $2$-step nilpotent torsion-free group.
Mots-clés : divisible group, torsion-free group 
@article{MZM_2015_97_6_a11,
     author = {S. A. Shakhova},
     title = {Absolutely {Closed} {Groups} in the {Class} of $2${-Step} {Nilpotent} {Torsion-Free} {Groups}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {936--941},
     publisher = {mathdoc},
     volume = {97},
     number = {6},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2015_97_6_a11/}
}
TY  - JOUR
AU  - S. A. Shakhova
TI  - Absolutely Closed Groups in the Class of $2$-Step Nilpotent Torsion-Free Groups
JO  - Matematičeskie zametki
PY  - 2015
SP  - 936
EP  - 941
VL  - 97
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2015_97_6_a11/
LA  - ru
ID  - MZM_2015_97_6_a11
ER  - 
%0 Journal Article
%A S. A. Shakhova
%T Absolutely Closed Groups in the Class of $2$-Step Nilpotent Torsion-Free Groups
%J Matematičeskie zametki
%D 2015
%P 936-941
%V 97
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2015_97_6_a11/
%G ru
%F MZM_2015_97_6_a11
S. A. Shakhova. Absolutely Closed Groups in the Class of $2$-Step Nilpotent Torsion-Free Groups. Matematičeskie zametki, Tome 97 (2015) no. 6, pp. 936-941. http://geodesic.mathdoc.fr/item/MZM_2015_97_6_a11/