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 
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     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://archive.numdam.org/articles/10.4171/RSMUP/3/}
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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://archive.numdam.org/articles/10.4171/RSMUP/3/

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