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.
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Russian Text © The Author(s), 2019, published in Sibirskii Matematicheskii Zhurnal, 2019, Vol. 60, No. 3, pp. 483–488.
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Azarov, D.N., Romanovskii, N.S. Finite Homomorphic Images of Groups of Finite Rank. Sib Math J 60, 373–376 (2019). https://doi.org/10.1134/S0037446619030017
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DOI: https://doi.org/10.1134/S0037446619030017