Geodesic
Properties of covers in the lattice of group topologies for nilpotent groups
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2012), pp. 38-44 
V. I. Arnautov. Properties of covers in the lattice of group topologies for nilpotent groups. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2012), pp. 38-44. http://geodesic.mathdoc.fr/item/BASM_2012_3_a3/
@article{BASM_2012_3_a3,
     author = {V. I. Arnautov},
     title = {Properties of covers in the lattice of group topologies for nilpotent groups},
     journal = {Buletinul Academiei de \c{S}tiin\c{t}e a Republicii Moldova. Matematica},
     pages = {38--44},
     year = {2012},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BASM_2012_3_a3/}
}
TY  - JOUR
AU  - V. I. Arnautov
TI  - Properties of covers in the lattice of group topologies for nilpotent groups
JO  - Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
PY  - 2012
SP  - 38
EP  - 44
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/BASM_2012_3_a3/
LA  - en
ID  - BASM_2012_3_a3
ER  - 
%0 Journal Article
%A V. I. Arnautov
%T Properties of covers in the lattice of group topologies for nilpotent groups
%J Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
%D 2012
%P 38-44
%N 3
%U http://geodesic.mathdoc.fr/item/BASM_2012_3_a3/
%G en
%F BASM_2012_3_a3

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

A nilpotent group $\widehat G$ and two group topologies $\widehat\tau''$ and $\widehat\tau*$ on $\widehat G$ are constructed such that $\widehat\tau*$ is a coatom in the lattice of all group topologies of the group $\widehat G$ and such that between $\inf\{\widehat\tau'',\widehat\tau_d\}$ and $\inf\{\widehat\tau'',\widehat\tau*\}$ there exists an infinite chain of group topologies.

[1] Arnautov V. I., Topala A. Gh., “An example of ring with non-modular lattice of ring topologies”, Bul. Acad. Ştiinţe Repub. Moldova, Mat., 1998, no. 2(27), 130–131 | MR | Zbl

[2] Arnautov V. I., “Properties of finite unrefinable chais of groups topologies”, Bul. Acad. Ştiinţe Repub. Moldova, Mat., 2009, no. 2(60), 1–17 | MR

[3] Bourbaki N., Obshchaya topologiya. Osnovnye structury (General Topology, Fundamental Structures), Moscow, 1958, 324 pp. (in Russian)