On the Conjugacy Separability of Generalized Free Products of Groups

TL;DR

This paper investigates conditions under which generalized free products of groups are conjugacy p-separable, establishing a key equivalence for finite p-groups and providing criteria for infinite groups.

Contribution

It proves that generalized free products of finite p-groups are conjugacy p-separable if and only if they are residually finite p-groups, and offers sufficient conditions for infinite groups.

Findings

Finite p-group free products are conjugacy p-separable iff residually finite p-groups.

Provides criteria for conjugacy p-separability in infinite group free products.

Establishes a fundamental equivalence linking conjugacy separability and residual finiteness.

Abstract

It is proved that generalized free product of two finite p-groups is a conjugacy p-separable group if and only if it is residually finite p-groups. This result is then applied to establish some sufficient conditions for conjugacy p-separability of generalized free product of infinite groups.