Countable recognizability and residual properties of groups
de Giovanni, Francesco1 ; Trombetti, Marco1
1 Università degli Studi di Napoli Federico II, Italy
Rendiconti del Seminario Matematico della Università di Padova, Tome 140 (2018), pp. 69-80.

A class of groups 𝔛 is said to be countably recognizable if a group belongs to 𝔛 whenever all its countable subgroups lie in 𝔛. It is proved here that the class of groups whose subgroups are closed in the profinite topology is countably recognizable. Moreover, countably detectable properties of the finite residual of a group are studied.

Publié le :
DOI : 10.4171/RSMUP/3
Classification : 20, 53
Mots-clés : Countably recognizable class, closed subgroup, finite residual
de Giovanni, Francesco 1 ; Trombetti, Marco 1

1 Università degli Studi di Napoli Federico II, Italy 
@article{RSMUP_2018__140__69_0,
     author = {de Giovanni, Francesco and Trombetti, Marco},
     title = {Countable recognizability and residual properties of groups},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     pages = {69--80},
     publisher = {European Mathematical Society Publishing House},
     address = {Zuerich, Switzerland},
     volume = {140},
     year = {2018},
     doi = {10.4171/RSMUP/3},
     mrnumber = {3880212},
     zbl = {1472.20064},
     url = {http://www.numdam.org/articles/10.4171/RSMUP/3/}
}
TY  - JOUR
AU  - de Giovanni, Francesco
AU  - Trombetti, Marco
TI  - Countable recognizability and residual properties of groups
JO  - Rendiconti del Seminario Matematico della Università di Padova
PY  - 2018
SP  - 69
EP  - 80
VL  - 140
PB  - European Mathematical Society Publishing House
PP  - Zuerich, Switzerland
UR  - http://www.numdam.org/articles/10.4171/RSMUP/3/
DO  - 10.4171/RSMUP/3
ID  - RSMUP_2018__140__69_0
ER  - 
%0 Journal Article
%A de Giovanni, Francesco
%A Trombetti, Marco
%T Countable recognizability and residual properties of groups
%J Rendiconti del Seminario Matematico della Università di Padova
%D 2018
%P 69-80
%V 140
%I European Mathematical Society Publishing House
%C Zuerich, Switzerland
%U http://www.numdam.org/articles/10.4171/RSMUP/3/
%R 10.4171/RSMUP/3
%F RSMUP_2018__140__69_0
de Giovanni, Francesco; Trombetti, Marco. Countable recognizability and residual properties of groups. Rendiconti del Seminario Matematico della Università di Padova, Tome 140 (2018), pp. 69-80. doi : 10.4171/RSMUP/3. http://www.numdam.org/articles/10.4171/RSMUP/3/

Cité par Sources :