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- W4300521504 abstract "If G is a finitely generated powerful pro-p group satisfying a certain law v=1, and if G can be generated by a normal subset T of finite width which satisfies a positive law, we prove that G is nilpotent. Furthermore, the nilpotency class of G can be bounded in terms of the prime p, the number of generators of G, the law v=1, the width of T, and the degree of the positive law. The main interest of this result is the application to verbal subgroups: if G is a p-adic analytic pro-p group in which all values of a word w satisfy positive law, and if the verbal subgroup w(G) is powerful, then w(G) is nilpotent." @default.
- W4300521504 created "2022-10-03" @default.
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- W4300521504 date "2011-08-02" @default.
- W4300521504 modified "2023-09-23" @default.
- W4300521504 title "Positive laws on generators in powerful pro-p groups" @default.
- W4300521504 doi "https://doi.org/10.48550/arxiv.1108.0547" @default.
- W4300521504 hasPublicationYear "2011" @default.
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