Abstract:The semidirect product of a group A by a group B is necessarily nilpotent only in the case A and B are p-groups for the same prime p, A is nilpotent of bounded exponent, and B is finite. In an earlier paper Morley has established an upper bound on the class of a nilpotent semidirect product of an abelian p-group of bounded exponent by an arbitrary finite p-group. In this paper this result is improved by considering a direct product decomposition for B and also by extending the results to give a new upper bound on the class in the most general case. The standard wreath product of A by B is a nilpotent semidirect product of relatively large class in the case A and B satisfy the conditions above, and this new bound improves the known results on the class of these wreath products.
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- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 60 (1976), 53-56
- MSC: Primary 20D40
- DOI: https://doi.org/10.1090/S0002-9939-1976-0427470-3
- MathSciNet review: 0427470