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Let $G$ be a finitely generated profinite group, and $H \leq_o G$. We say that $H$ satisfies Schreier's formula in $G$ if $d(H) - 1 = (d(G)-1)[G:H]$. We say that $G$ satisfies Schreier's formula if ...

Let $A,B$ be finitely generated groups with a common finite subgroup $C$. Suppose that $[A : C] > 2, [B : C] > 1$. Must $A *_C B$ have positive rank gradient? See Which 3-manifolds have ...

This is an attempt to find a correct version of Do free profinite groups satisfy Howson's theorem? Let $F$ be a free profinite group, and let $A,B \leq F$ be closed finitely generated subgroups ...