Finite Homomorphic Images of Groups of Finite Rank Full article
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Siberian Mathematical Journal
ISSN: 0037-4466 , E-ISSN: 1573-9260 |
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| Output data | Year: 2019, Volume: 60, Number: 3, Pages: 373-376 Pages count : 4 DOI: 10.1134/S0037446619030017 | ||||||
| Tags | group of finite rank; homomorphic image of a group; profinite group; residual finiteness; soluble group | ||||||
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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. © 2019, Pleiades Publishing, Inc.
Cite:
Azarov D.N.
, Romanovskii N.S.
Finite Homomorphic Images of Groups of Finite Rank
Siberian Mathematical Journal. 2019. V.60. N3. P.373-376. DOI: 10.1134/S0037446619030017 WOS Scopus OpenAlex
Finite Homomorphic Images of Groups of Finite Rank
Siberian Mathematical Journal. 2019. V.60. N3. P.373-376. DOI: 10.1134/S0037446619030017 WOS Scopus OpenAlex
Identifiers:
| Web of science: | WOS:000471617300001 |
| Scopus: | 2-s2.0-85067294069 |
| OpenAlex: | W2952716200 |