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A well known lemma of Burnside is generalised, to give necessary and sufficient conditions for a finite p-group K to be normally embedded in a nilpotent group V, with Ksco(K). (Here, u> denotes a single word and co(V) is the corresponding verbal subgroup.) Our main result is related to earlier work of Blackburn, Gaschutz and Hobby. 1980 Mathematics subject classification (1985 Revision). 20D15, 20E22.doi:10.1017/s0013091500005575 fatcat:egccneqwg5dk5diri6424lsfpm