Finite Homomorphic Images of Groups of Finite Rank
- Авторы: Azarov D.1, Romanovskii N.2
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Учреждения:
- Ivanovo State University
- Sobolev Institute of Mathematics
- Выпуск: Том 60, № 3 (2019)
- Страницы: 373-376
- Раздел: Article
- URL: https://journals.rcsi.science/0037-4466/article/view/172380
- DOI: https://doi.org/10.1134/S0037446619030017
- ID: 172380
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Аннотация
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.
Об авторах
D. Azarov
Ivanovo State University
Автор, ответственный за переписку.
Email: azarovdn@mail.ru
Россия, Ivanovo
N. Romanovskii
Sobolev Institute of Mathematics
Автор, ответственный за переписку.
Email: rmnvski@math.nsc.ru
Россия, Novosibirsk