Varieties of solvable pro-p-groups
type: Item
instance of: scholarly article
title: Varieties of solvable pro-p-groups
zbMATH Open document ID: 0543.20020
DOI: 10.1007/BF01979676
author: A. F. Krasnikov
published in: Algebra and Logic
publication date: 1983-01-01T00:00:00Z
review text: Let \({\mathfrak B}_ m\) be the variety of groups of exponent m and let \({\mathfrak N}_ c\) be the variety of nilpotent groups with nilpotence degree \(\leq c\). It is proved that the variety of soluble pro-p-groups, not containing all metabelian groups, is a subvariety in \({\mathfrak B}_{p^ n}{\mathfrak N}_ c{\mathfrak B}_{p^ n}\) for some n and c. This theorem is parallel to a result of \textit{M. Kargapolov} and \textit{V. Churkin} [Algebra Logika 10, 651-657 (1971; Zbl 0258.20033)]. The author gives also a description (see Th. 5.1) of the class of finitely generated soluble pro-p-groups of finite rank.
Mathematics Subject Classification ID: 20E10
Mathematics Subject Classification ID: 20E18
Mathematics Subject Classification ID: 20F16
Mathematics Subject Classification ID: 20F18
zbMATH DE Number: 3863459
zbMATH Keywords: variety of nilpotent groups
zbMATH Keywords: variety of soluble pro-p-groups
zbMATH Keywords: finitely generated soluble pro-p-groups
reviewed by: U. Kaljulaid
MaRDI profile type: Publication
cites work: Q3964761
cites work: On varieties of soluble groups II
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description: scientific article; zbMATH DE number 3863459