Geodesic
Adjunction of roots to nilpotent groups
Glasgow mathematical journal, Tome 7 (1966) no. 3, pp. 109-118

Voir la notice de l'article provenant de la source Cambridge University Press

For any nilpotent group B of class c and any given element h of B generating the subgroup H, Wiegold [1] has shown that if, in addition, [B, H] has exponent pr for some prime p and integer r, then B can be embedded in a nilpotent group G such that G also contains psth root for h(s ≧ 1). In fact, Wiegold has gone further and calculated an upper bound for the class of G in terms of the variables c, p, r, s. 
Allenby, R. B. J. T. Adjunction of roots to nilpotent groups. Glasgow mathematical journal, Tome 7 (1966) no. 3, pp. 109-118. doi: 10.1017/S2040618500035280
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[1] 1.Wiegold, J., Adjunction of elements to nilpotent groups, J. London. Math. Soc. 38 (1963), 17–26. Google Scholar | DOI

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