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Embedding theorems for pro-p groups
Published online by Cambridge University Press: 01 March 1998
Abstract
Baumslag [Bm1] and Remeslennikov [R1] independently showed that the abstract group with finite presentation
〈a, x, y[mid ]ax =aay, [x, y] =1=[a, ay]〉.
is metabelian; the derived subgroup is free abelian of countably infinite rank. Both generalized this example to show that every finitely generated metabelian group embeds in a finitely presented metabelian group. Thomson [T] generalized this result still further to show that every finitely generated group of upper triangular matrices over an abstract ring A lies inside a finitely presented group of upper triangular matrices over some extension ring of A. For a valuable survey of these results, see [St].
Baumslag proved analogous theorems for Lie algebras in [Bm2]. In this paper we shall prove some analogous results for pro-p groups.
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- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 123 , Issue 2 , March 1998 , pp. 217 - 226
- Copyright
- Cambridge Philosophical Society 1998
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