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