March 3, 2026

On the Root-Class Residuality of Tree Products of Groups with Normal Edge Subgroups

Key Points

Homomorphisms from tree products can map injectively onto root class groups, enhancing understanding of group structures.
Existential conditions for $ ext{C}$-homomorphisms were established, focusing on normal subgroup dynamics.
The concept of residuality addresses group characteristics when normal edge subgroups interact with vertex groups.
Sufficient conditions show that tree product structure significantly influences subgroup properties and mappings.

Abstract

Let C be a root class of groups, i. e. , a class containing nontrivial groups and closed under taking subgroups and Cartesian wreath products. Let also P be a tree product of groups such that each edge subgroup of P is normal in the vertex group that includes it. The paper presents several sufficient conditions for the existence of a homomorphism from the group P onto a C -group that is injective on all vertex groups. Some sufficient conditions for the C -residuality of the group P are also proved.

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On the Root-Class Residuality of Tree Products of Groups with Normal Edge Subgroups

Key Points

Abstract

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