Open AccessOn the Residual Finiteness of Some Generalized Products of Soluble Groups of Finite Rank
Author(s) -
Алексей Вячеславович Розов
Publication year - 2015
Publication title -
modelirovanie i analiz informacionnyh sistem
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.