Finite Homomorphic Images of Groups of Finite Rank
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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.
Keywordsgroup of finite rank soluble group homomorphic image of a group residual finiteness profinite group
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