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- Title
On the Approximability by Finite p-Groups of Free Products of Groups with Normal Amalgamation.
- Authors
Sokolov, E. V.
- Abstract
A sufficient condition for the residual p-finiteness (approximability by the class $$\mathcal{F}_p$$ of finite p-groups) of a free product G = ( A * B; H) of groups A and B with a normal amalgamated subgroup H is obtained. This condition is used to prove that if A and B are extensions of residually $$\mathcal{N}$$ -groups by $$\mathcal{F}_p$$ -groups, where $$\mathcal{N}$$ stands for the class of finitely generated torsion-free nilpotent groups, and if H is a normal p′-isolated polycyclic subgroup, then the group G is residually p-finite (i.e., residually $$\mathcal{F}_p$$ -group), provided the quotient group G/H p H′ is residually p-finite.
- Subjects
APPROXIMATION theory; FINITE groups; NILPOTENT groups; FUNCTIONAL analysis; POLYNOMIALS; MATHEMATICAL functions
- Publication
Mathematical Notes, 2005, Vol 78, Issue 1/2, p114
- ISSN
0001-4346
- Publication type
Article
- DOI
10.1007/s11006-005-0104-1