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On Solvable Groups of Exponent 4

Authors
  • Deryabina, G. S.1
  • Krasil'nikov, A. N.2
  • 1 Heriot-Watt University, Edinburgh , Edinburgh
  • 2 Moscow State Pedagogical University, Russia
Type
Published Article
Journal
Siberian Mathematical Journal
Publisher
Kluwer Academic Publishers-Plenum Publishers
Publication Date
Jan 01, 2003
Volume
44
Issue
1
Pages
58–60
Identifiers
DOI: 10.1023/A:1022060219947
Source
Springer Nature
Keywords
License
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Abstract

Given an arbitrary identity v=1, there exists a positive integer N=N(v) such that for every metabelian group G and every generating set A for G the following holds: If each subgroup of G generated by at most N elements of A satisfies the identity v=1 then the group G itself satisfies this identity. A similar assertion fails for center-by-metabelian groups. This answers Bludov's question.

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