# Tagged Questions

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### Normal Subgroup Growth

Let $F$ be a free group on $d$ generators. Denote by $F_{k}$ the $k$-th term in $F$'s derived series. Put $G = F/F_k$. What is the normal subgroup growth of $G$? Explicitly, for each natural number ...
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### Schreier's index formula

A finitely generated group G is said to satisfy Schreier's index formula if for every subgroup H of index k in G we have: d(H) - 1 = k(d(G) - 1). For example, a finitely generated free group satisfies ...
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### “Concretely” writing down elements in a free profinite group

Let $r$ be a natural number. The elements of the free group $F_r$ on $r$ generators have a nice concrete description as "words" in the $r$ generators (and their inverses). I'd like to know if there is ...
### How to determine free generators of a closed subgroup of a free pro-$p$-group ?
If $F$ is a free discrete group, then any subgroup $H$ of $F$ is free: this is the well-known theorem of Nielsen-Schreier. Moreover, there is a well-known algorithm, the Nielsen-Schreier method that ...
I don't know much about free groups (excepted the very basics), and the following question may be trivial, although it isn't to me. Let $F$ be a free group with $n$ generators $x_1,\dots,x_n$. ...