Generating numbers for wreath products (Q1891519)

For any group \(G\), \(d(G)\) denotes the minimal number of generators. For groups \(A\), \(B\), \(A\wr B\) denotes the wreath product of \(A\) by \(B\). The author proves the following Theorem: For every positive integer \(m\) there exists a group \(A\) with \(d(A)=m\) and a cyclic group \(B\) such that \(d(A\wr B)=2\).