A bound for the number of one-relator groups of corank 1 (Q1275994)

\textit{J. R. Stallings} [Ohio State Univ. Math. Res. Inst. Publ. 3, 165-182 (1995; Zbl 0869.20012)] introduced the notion of group corank. Let \(F_n\) be a free group of rank \(n\) and \(L_n(m)\) be the number of elements of \(F_n\) represented by nonreducible words of length \(m\) (\(L_n(m)=2n\cdot(2n-1)^{m-1}\) for \(m\geq 1\)). The author proves the following theorem: Let \(n\) be a natural number, \(n\geq 2\). Then there exist a positive number \(\Delta=\Delta(n)\) and a natural number \(m_0=m_0(n)\) such that for any \(m>m_0\) among all nonreducible words \(w\) of length \(m\) from \(F_n\) at least \(\Delta\cdot L_n(m)\) are such that \(\text{corank}\langle x_1,\dots,x_n\rangle=1\).