 Rank-to-index limit for subgroups of a free group (source code)

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= Rank-to-index limit for subgroups of a free group
{title2=$\operatorname{rank}(H)/[F_n:H]=n-1+1/[F_n:H]$}

For finite-index subgroups of a rank-$n$ <free group>, the <Nielsen–Schreier formula> gives the displayed quotient. Along any sequence whose finite indices tend to infinity, the quotient tends to $n-1$. Subtracting one from the rank before dividing gives the constant rank gradient $n-1$.

// Target: geometry-and-topology.bigb

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