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Siberian Mathematical Journal

, Volume 60, Issue 3, pp 373–376 | Cite as

Finite Homomorphic Images of Groups of Finite Rank

  • D. N. AzarovEmail author
  • N. S. RomanovskiiEmail author
Article
  • 13 Downloads

Abstract

Let π be a finite set of primes. We prove that each soluble group of finite rank contains a finite index subgroup whose every finite homomorphic π-image is nilpotent. A similar assertion is proved for a finitely generated group of finite rank. These statements are obtained as a consequence of the following result of the article: Each soluble pro-π-group of finite rank has an open normal pronilpotent subgroup.

Keywords

group of finite rank soluble group homomorphic image of a group residual finiteness profinite group 

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Copyright information

© Pleiades Publishing, Inc. 2019

Authors and Affiliations

  1. 1.Ivanovo State UniversityIvanovoRussia
  2. 2.Sobolev Institute of MathematicsNovosibirsk State UniversityNovosibirskRussia

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