Standard

Finite Homomorphic Images of Groups of Finite Rank. / Azarov, D. N.; Romanovskii, N. S.

In: Siberian Mathematical Journal, Vol. 60, No. 3, 01.05.2019, p. 373-376.

Research output: Contribution to journal › Article › peer-review

Harvard

Azarov, DN & Romanovskii, NS 2019, 'Finite Homomorphic Images of Groups of Finite Rank', Siberian Mathematical Journal, vol. 60, no. 3, pp. 373-376. https://doi.org/10.1134/S0037446619030017

APA

Azarov, D. N., & Romanovskii, N. S. (2019). Finite Homomorphic Images of Groups of Finite Rank. Siberian Mathematical Journal, 60(3), 373-376. https://doi.org/10.1134/S0037446619030017

Vancouver

Azarov DN, Romanovskii NS. Finite Homomorphic Images of Groups of Finite Rank. Siberian Mathematical Journal. 2019 May 1;60(3):373-376. doi: 10.1134/S0037446619030017

Author

Azarov, D. N. ; Romanovskii, N. S. / Finite Homomorphic Images of Groups of Finite Rank. In: Siberian Mathematical Journal. 2019 ; Vol. 60, No. 3. pp. 373-376.

BibTeX

@article{020ac7509cd941cfbc31629eac6df859,
title = "Finite Homomorphic Images of Groups of Finite Rank",
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, homomorphic image of a group, profinite group, residual finiteness, soluble group",
author = "Azarov, {D. N.} and Romanovskii, {N. S.}",
year = "2019",
month = may,
day = "1",
doi = "10.1134/S0037446619030017",
language = "English",
volume = "60",
pages = "373--376",
journal = "Siberian Mathematical Journal",
issn = "0037-4466",
publisher = "MAIK NAUKA/INTERPERIODICA/SPRINGER",
number = "3",

}

RIS

TY - JOUR

T1 - Finite Homomorphic Images of Groups of Finite Rank

AU - Azarov, D. N.

AU - Romanovskii, N. S.

PY - 2019/5/1

Y1 - 2019/5/1

N2 - 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.

AB - 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.

KW - group of finite rank

KW - homomorphic image of a group

KW - profinite group

KW - residual finiteness

KW - soluble group

UR - http://www.scopus.com/inward/record.url?scp=85067294069&partnerID=8YFLogxK

U2 - 10.1134/S0037446619030017

DO - 10.1134/S0037446619030017

M3 - Article

AN - SCOPUS:85067294069

VL - 60

SP - 373

EP - 376

JO - Siberian Mathematical Journal

JF - Siberian Mathematical Journal

SN - 0037-4466

IS - 3

ER -

ID: 20591090