Geodesic
Topological prime radical of a~group
Fundamentalʹnaâ i prikladnaâ matematika, Tome 10 (2004) no. 4, pp. 15-22.

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

In this paper, we consider two approaches for the definition of a topological prime radical of a topological group. In the first approach, the prime quasi-radical $\eta(G)$ is defined as the intersection of all closed prime normal subgroups of a topological group $G$. Its properties are investigated. In the second approach, we consider the set $\eta'(G)$ of all topologically strictly Engel elements of a topological group $G$. Its properties are investigated. It is proved that $\eta'(G)$ is a radical in the class of all topological groups possessing a basis of neighborhoods of the identity element consisting of normal subgroups. 
@article{FPM_2004_10_4_a1,
     author = {B. Bazigaran and S. T. Glavatskii and A. V. Mikhalev},
     title = {Topological prime radical of a~group},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {15--22},
     publisher = {mathdoc},
     volume = {10},
     number = {4},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2004_10_4_a1/}
}
TY  - JOUR
AU  - B. Bazigaran
AU  - S. T. Glavatskii
AU  - A. V. Mikhalev
TI  - Topological prime radical of a~group
JO  - Fundamentalʹnaâ i prikladnaâ matematika
PY  - 2004
SP  - 15
EP  - 22
VL  - 10
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FPM_2004_10_4_a1/
LA  - ru
ID  - FPM_2004_10_4_a1
ER  - 
%0 Journal Article
%A B. Bazigaran
%A S. T. Glavatskii
%A A. V. Mikhalev
%T Topological prime radical of a~group
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 2004
%P 15-22
%V 10
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FPM_2004_10_4_a1/
%G ru
%F FPM_2004_10_4_a1
B. Bazigaran; S. T. Glavatskii; A. V. Mikhalev. Topological prime radical of a~group. Fundamentalʹnaâ i prikladnaâ matematika, Tome 10 (2004) no. 4, pp. 15-22. http://geodesic.mathdoc.fr/item/FPM_2004_10_4_a1/

[1] Andrunakievich V. A., “Radikaly assotsiativnykh kolets, II”, Mat. sb., 55(97) (1961), 329–346

[2] Burbaki N., Obschaya topologiya. Topologicheskie gruppy, chisla, IL, M., 1969

[3] Kurosh A. G., “Radikaly v teorii grupp”, DAN, 141:4 (1961), 789–791 | Zbl

[4] Kurosh A. G., Teoriya grupp, Nauka, M., 1967 | MR | Zbl

[5] Khuzurbazar M. Sh., “Multiplikativnaya gruppa tela”, DAN, 131:6 (1960), 1268–1271 | Zbl

[6] Schukin K. K., “$RI^{*}$-razreshimyi radikal grupp”, DAN, 132 (1960), 541–544 | Zbl

[7] Schukin K. K., “K teorii radikalov v gruppakh”, DAN, 142:5 (1962), 1047–1049 | Zbl

[8] Schukin K. K., Radikaly grupp, Diss. $\dots$ kand. fiz.-mat. nauk, 1962

[9] Arnautov V. I., Glavatsky S. T., Mikhalev A. V., Introduction to the Theory of Topological Rings and Modules, Marcel Dekker, New York, 1996 | MR | Zbl