About group topologies of the primary Abelian group of finite period which coincide on a subgroup and on the factor group
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2009), pp. 19-28
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Let $G$ be any Abelian group of the period $p^n$ and $G_1=\{g\in G\mid pg=0\}$, $G_2=\{g\in G\mid p^{n-1}g=0\}$. If $\tau$ and $\tau'$ are a metrizable, linear group topologies such that $G_2$ is a closed subgroup in each of topological groups $(G,\tau)$ and $(G,\tau')$, then $\tau|_{G_2}=\tau'|_{G_2}$ and $(G,\tau)/G_1=(G,\tau')/G_1$ if and only if there exists a group isomorphism $\varphi\colon G\to G$ such that the following conditions are true: 1. $\varphi(G_2)=G_2$; 2. $g-\varphi(g)\in G_1$ for any $g\in G$; 3. $\varphi\colon (G,\tau)\to(G,\tau')$ is a topological isomorphism.
@article{BASM_2009_2_a1,
author = {V. I. Arnautov},
title = {About group topologies of the primary {Abelian} group of finite period which coincide on a~subgroup and on the factor group},
journal = {Buletinul Academiei de \c{S}tiin\c{t}e a Republicii Moldova. Matematica},
pages = {19--28},
year = {2009},
number = {2},
language = {en},
url = {http://geodesic.mathdoc.fr/item/BASM_2009_2_a1/}
}
TY - JOUR AU - V. I. Arnautov TI - About group topologies of the primary Abelian group of finite period which coincide on a subgroup and on the factor group JO - Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica PY - 2009 SP - 19 EP - 28 IS - 2 UR - http://geodesic.mathdoc.fr/item/BASM_2009_2_a1/ LA - en ID - BASM_2009_2_a1 ER -
%0 Journal Article %A V. I. Arnautov %T About group topologies of the primary Abelian group of finite period which coincide on a subgroup and on the factor group %J Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica %D 2009 %P 19-28 %N 2 %U http://geodesic.mathdoc.fr/item/BASM_2009_2_a1/ %G en %F BASM_2009_2_a1
V. I. Arnautov. About group topologies of the primary Abelian group of finite period which coincide on a subgroup and on the factor group. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2009), pp. 19-28. http://geodesic.mathdoc.fr/item/BASM_2009_2_a1/