During the 1970s a series of impressive papers by Razmyslov settled the problem of the solvability of the Burnside variety \(B_ k\), that is, the variety of groups satisfying the law \(x^ k=1\). It has long been known that for \(k=2,3,6\) the groups in \(B_ k\) are solvable of length (at most) 1,2,3 respectively. Razmyslov exhibited non-solvable groups in \(B_ k\) for all other values of \(k>1.\) In this expository paper the author presents a very readable version of \textit{Yu. P. Razmyslov}'s construction in the case \(k=p^ 2\), p an odd prime. The primary source is Izv. Akad. Nauk. SSSR., Ser. Mat. 42, 833- 847 (1978; Zbl 0394.20030), with a translation by J. Wiegold in Math. USSR, Izv. 13, 133-146 (1979). The author's main aim in the exposition is to convey some idea of Razmyslov's methods, but he remarks that this may encourage the reader to delve into the far more complex details of the case \(k=4.\) The tools used are Lie-ring-theoretic and the treatment is refreshingly clear. We could do with many more articles of this kind.