Finite Homomorphic Images of Groups of Finite Rank
- Authors: Azarov D.N.1, Romanovskii N.S.2
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Affiliations:
- Ivanovo State University
- Sobolev Institute of Mathematics
- Issue: Vol 60, No 3 (2019)
- Pages: 373-376
- Section: Article
- URL: https://journals.rcsi.science/0037-4466/article/view/172380
- DOI: https://doi.org/10.1134/S0037446619030017
- ID: 172380
Cite item
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.
About the authors
D. N. Azarov
Ivanovo State University
Author for correspondence.
Email: azarovdn@mail.ru
Russian Federation, Ivanovo
N. S. Romanovskii
Sobolev Institute of Mathematics
Author for correspondence.
Email: rmnvski@math.nsc.ru
Russian Federation, Novosibirsk