On the Residual Finiteness of Some Generalized Products of Soluble Groups of Finite Rank | Zendy

A. V. Rozov | Zendy

AI Assistant Blog Pricing

Home ZAIA Blog

Open Access

On the Residual Finiteness of Some Generalized Products of Soluble Groups of Finite Rank

Author(s) -

A. V. Rozov

Publication year - 2015

Publication title -

modeling and analysis of information systems

Language(s) - English

Resource type - Journals

eISSN - 2313-5417

pISSN - 1818-1015

DOI - 10.18255/1818-1015-2013-1-124-132

Subject(s) - mathematics , rank (graph theory) , separable space , finitely generated abelian group , combinatorics , group (periodic table) , normal subgroup , chemistry , mathematical analysis , organic chemistry

Let G be a free product of residually finite virtually soluble groups A and B of finite rank with an amalgamated subgroup H, H 6= A and H 6= B. And let H contains a subgroup W of finite index which is normal in both A and B. We prove that the group G is residually finite if and only if the subgroup H is finitely separable in A and B. Also we prove that if all subgroups of A and B are finitely separable in A and B, respectively, all finitely generated subgroups of G are finitely separable in G.

The content you want is available to Zendy users.

Already have an account? Click here to sign in.

Having issues? You can contact us here

Accelerating Research