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- W2054883886 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." @default.
- W2054883886 created "2016-06-24" @default.
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- W2054883886 date "1976-01-01" @default.
- W2054883886 modified "2023-09-25" @default.
- W2054883886 title "An improvement on the upper bound of the nilpotency class of semidirect products of $p$-groups" @default.
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- W2054883886 doi "https://doi.org/10.1090/s0002-9939-1976-0427470-3" @default.
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