Groups generated by elements of small breadth (Q2747312)

\textit{M.~R.~Vaughan-Lee} and \textit{J.~Wiegold} [Proc. R. Soc. Edinb., Sect. A 95, 215-221 (1983; Zbl 0524.20008)] have shown that if a finite \(p\)-group \(G\) can be generated by elements of breadth \(k\), then the nilpotency class \(\text{cl}(G)\) of \(G\) is at most \(k^2+1\). Here an element \(x\in G\) is said to be of breadth \(k\) if its conjugacy class has size \(p^k\). Recently, a new proof of this result has been provided by \textit{C.~Warren} and \textit{J.~Wiegold} [J. Group Theory 2, No.~4, 373-375 (1999; Zbl 0941.20014)]. In his review MR 85i:20023 for Mathematical Reviews of the paper by Vaughan-Lee and Wiegold, the author of the paper under review claimed the improved estimate \(\text{cl}(G)\leq k^2-k+1\). The goal of the paper under review is to record a proof for this estimate. We refer to the original paper for further comments and other interesting results.