An insoluble (p−2)-Engel group of exponent p

In 1971 Razmyslov [4], found a beautiful construction for insoluble, locally nilpotent groups of exponent p (p⩾5). In 1978 Razmyslov [5] refined his construction, and showed that it also gives insoluble groups of exponent 4. In this note we show that Razmyslov's method can be used to construct insoluble, locally nilpotent, (p−2)-Engel groups of exponent p for all primes p⩾5.