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/

[1] J. R. Isbell, “Epimorphisms and dominions”, Proceedings of the Conference on Categorical Algebra, Springer, New York, 1966, 232–246 | MR

[2] A. Budkin, “Dominions in quasivarieties of universal algebras”, Studia Logica, 78:1-2 (2004), 107–127 | DOI | MR | Zbl

[3] P. M. Higgins, “Epimorphisms and amalgams”, Colloq. Math., 56:1 (1988), 1–17 | MR | Zbl

[4] A. I. Budkin, “Reshetki dominionov universalnykh algebr”, Algebra i logika, 46:1 (2007), 26–45 | MR | Zbl

[5] S. A. Shakhova, “O reshetkakh dominionov v kvazimnogoobraziyakh abelevykh grupp”, Algebra i logika, 44:2 (2005), 238–251 | MR | Zbl

[6] S. A. Shakhova, “Usloviya distributivnosti reshetok dominionov v kvazimnogoobraziyakh abelevykh grupp”, Algebra i logika, 45:4 (2006), 484–499 | MR | Zbl

[7] A. I. Budkin, “Dominiony universalnykh algebr i proektivnye svoistva”, Algebra i logika, 47:5 (2008), 541–557 | MR | Zbl

[8] A. Magidin, “Dominions in varieties of nilpotent groups”, Comm. Algebra, 28:3 (2000), 1241–1270 | DOI | MR | Zbl

[9] A. Magidin, “Absolutely closed nil-2 groups”, Algebra Universalis, 42:1-2 (1999), 61–77 | DOI | MR | Zbl

[10] A. I. Budkin, “O dominionakh v kvazimnogoobraziyakh metabelevykh grupp”, Sib. matem. zhurn., 51:3 (2010), 498–505 | MR | Zbl

[11] Nereshennye voprosy teorii grupp. Kourovskaya tetrad, 17-e izd., In-t matem. SO RAN, Novosibirsk, 2010

[12] M. I. Kargapolov, Yu. I. Merzlyakov, Osnovy teorii grupp, Nauka, M., 1972 | MR | Zbl

[13] A. G. Kurosh, Teoriya grupp, Lan, SPb., 2005 | MR | Zbl

[14] A. I. Maltsev, Algebraicheskie sistemy, Nauka, M., 1970 | MR | Zbl

[15] V. A. Gorbunov, Algebraicheskaya teoriya kvazimnogoobrazii, Sibirskaya shkola algebry i logiki, 5, Nauchnaya kniga, Novosibirsk, 1999 | Zbl

[16] A. I. Budkin, Kvazimnogoobraziya grupp, Izd-vo Altaiskogo un-ta, Barnaul, 2002

[17] A. I. Maltsev, “Nilpotentnye gruppy bez krucheniya”, Izv. AN SSSR. Ser. matem., 13:3 (1949), 201–212 | MR | Zbl

[18] A. A. Vinogradov, “Kvazimnogoobraziya abelevykh grupp”, Algebra i logika, 4:6 (1965), 15–19 | MR | Zbl

[19] A. N. Fedorov, “Kvazitozhdestva svobodnoi 2-nilpotentnoi gruppy”, Matem. zametki, 40:5 (1986), 590–597 | MR | Zbl

[20] E. S. Polovnikova, “Ob aksiomaticheskom range kvazimnogoobrazii”, Sib. matem. zhurn., 40:1 (1999), 167–176 | MR | Zbl