Timeline for Countable group with uncountable number of subgroups $< 2^{\aleph_0}$ [duplicate]

7 events

when toggle format	what		by	license	comment
Jan 9, 2019 at 18:07	history	closed	YCor gr.group-theory		Duplicate of Finitely generated group with $\aleph_0<X_G<2^{\aleph_0}$ normal subgroups?
Jun 18, 2015 at 6:38	vote	accept	Dominic van der Zypen
Jun 17, 2015 at 23:58	comment	added	user35370		YCor basically answers in this question, also there is some discussion of whether or not quotients could be uncountable but not $2^{\aleph_0}$. There seems, a priori, that a quotient could have $\aleph_1$ many elements, as pointed out by Emil, although I am not sure if there have been proofs that there are groups like that, (The question is not exactly the same, but YCor points out it works for subgroups)
Jun 17, 2015 at 15:17	answer	added	Emil Jeřábek		timeline score: 26
Jun 17, 2015 at 14:56	comment	added	Joel David Hamkins		Emil, why not post as an answer? Although the set theorists are accustomed to thinking of the class of countable groups as a Polish space, this might be less familiar to the group theorists, and so this may be a good opportunity to explain this perspective.
Jun 17, 2015 at 14:43	comment	added	Emil Jeřábek		No, the set of subgroups of $G$ is closed as a subset of the Polish space $2^G$.
Jun 17, 2015 at 14:22	history	asked	Dominic van der Zypen	CC BY-SA 3.0