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 Apr 12 comment Does $[G:N_G(H)]<\infty$ imply $[H:\text{Core}_G(H)]<\infty$ In the presentation above, I forgot the relation $c^2=1$. Apr 12 comment Does $[G:N_G(H)]<\infty$ imply $[H:\text{Core}_G(H)]<\infty$ No. For example, consider $\langle a,b,c\mid [a,b]=1, cac^{-1}=b, cbc^{-1}=a\rangle=(\mathbb{Z}\times\mathbb{Z})\rtimes{\mathbb{Z}/2}$. The only subgroup conjugate to $\langle a\rangle$ is $\langle b\rangle$, but $Core_G(\langle a\rangle)=1$. Feb 25 awarded Popular Question Feb 24 awarded Enlightened Feb 24 awarded Nice Answer Nov 15 awarded Yearling Aug 3 comment What finitely generated amenable groups are known to be LERF? Thank you very much for this excellent answer! Aug 3 accepted What finitely generated amenable groups are known to be LERF? Jul 31 asked What finitely generated amenable groups are known to be LERF? Jun 8 comment Is there a “uniform” Folner sequence consisting of balls for f.p. groups with polynomial growth? @YCor: Sorry for the inaccuracies. Did you mean $(b(r+1)-b(r))/b(r)=O(r^{-1})$? Jun 8 comment Is there a “uniform” Folner sequence consisting of balls for f.p. groups with polynomial growth? Is it possible to reduce the general case to the case of normal subgroups by taking a finite index normal subgroup of the not necessarily normal subgroup? I'm not sure - because running over different subgroups we get covers of unbounded degree (I mean: the Schreier graph of G/H covering the Cayley graph G/N for some N normal in G and contained in H). Jun 8 comment Is there a “uniform” Folner sequence consisting of balls for f.p. groups with polynomial growth? @YCor: Here's an idea: If the degree of the polynomial growth of $G$ is $d$, then (very nontrivially) the growth goes like $Cd^r$ for some constant $d$ (not only a upper bound, but almost exactly), and so the ratio $|\partial B(r)|/|B(r)|$ is at most $d/r$. For quotients the same is true with an even smaller (at least, not larger) degree $d$. Does this seem right? If so, then it settles the version of the question were we're only looking at quotients by normal subgroups, and we're left with generalizing to general subgroups (maybe this was obvious to you, I'm still a beginner in this field). Jun 7 comment Is there a “uniform” Folner sequence consisting of balls for f.p. groups with polynomial growth? @YCor: I know how to show that balls are Folner in groups of subexponential growth, but (the supremum version of) this question asks for more, doesn't it? I would like to know the answer too. Jun 7 comment Is there a “uniform” Folner sequence consisting of balls for f.p. groups with polynomial growth? @YCor: I too believe "supremum" was meant here, but note that $H$ only runs over finite index subgroups. Mar 28 accepted Finite dimensional central division algebras over a finite extension of $\mathbb{F}_q(T)$ Mar 28 comment Finite dimensional central division algebras over a finite extension of $\mathbb{F}_q(T)$ @KCd: Do you have a reference for that? Mar 28 asked Finite dimensional central division algebras over a finite extension of $\mathbb{F}_q(T)$ Mar 27 accepted Components in random graphs $G(n,p)$ Mar 24 asked Components in random graphs $G(n,p)$ Dec 27 awarded Nice Question