On the finitely separability of subgroups of generalized free products

TL;DR

This paper proves that finitely generated subgroups of certain generalized free products are finitely separable under specific conditions related to the properties of free factors and amalgamated subgroups.

Contribution

It establishes conditions ensuring the finite separability of finitely generated subgroups in generalized free products, extending previous results in group theory.

Findings

Finitely generated subgroups are finitely separable under given conditions.

Normality and maximum subgroup condition are crucial for separability.

Results apply to generalized free products with specific subgroup properties.

Abstract

It is proved that all finitely generated subgroups of generalized free product of two groups are finitely separable provided that free factors have this property and amalgamated subgroups are normal in corresponding factors and satisfy the maximum condition for subgroups.