Finite Homomorphic Images of Groups of Finite Rank

D. N. Azarov, N. S. Romanovskii

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Pages (from-to)373-376
Number of pages4
JournalSiberian Mathematical Journal
Volume60
Issue number3
DOIs
Publication statusPublished - 1 May 2019

Keywords

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

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