On exponential growth rates for free groups
It is well known that, with respect to any basis of a free group \(F_n\) of rank \(n\), the exponential growth rate is \(2n-1\). It is shown in the paper that the exponential growth rate of a group \(G\) with respect to an \(n\)-element generating set \(X\) is \(2n-1\) if and only if \(G\) is free on \(X\).
scientific article; zbMATH DE number 1267260