On the Root-Class Residuality of Tree Products of Groups with Normal Edge Subgroups
Abstract
Let $ {\mathcal{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 $ {\mathcal{C}} $ -group that is injective on all vertex groups. Some sufficient conditions for the $ {\mathcal{C}} $ -residuality of the group $ P $ are also proved.
Fields of Study & Subjects
Finite Group Theory Research
Geometric and Algebraic Topology
Advanced Topology and Set Theory
Publication details
- Journal / source
- Siberian Mathematical Journal
- Volume
- 67
- Issue
- 1
- Pages
- 125–141
- Publication date
- 1 January 2026
- Language
- EN