What question did this study set out to answer?

The aim is to explore the structural properties of commensurated subgroups and their relationship to cohomological dimensions.

March 28, 2026Annales de l’institut Fourier0 citationsOpen Access

View Full Paper

Groups of cohomological codimension one

Q: What does this research mean for the field?

If a commensurated subgroup H and a group G are both of type VFP and the virtual cohomological dimension of G is exactly one greater than that of H, then G is the fundamental group of a graph of groups in which all vertex and edge groups are commensurable to H. Novelty: ClaimNovelty.NOVEL_FINDING. Consensus alignment: ConsensusAlignment.NEUTRAL.

AMAlexander Margolis

Key Points

The aim is to explore the structural properties of commensurated subgroups and their relationship to cohomological dimensions.
Investigating the properties of commensurated subgroups in groups of type VFP.
Analyzing the relationship between the virtual cohomological dimensions of groups H and G.
Studying specific cases involving one-relator groups and duality groups.
Demonstrated that if group G has a commensurated subgroup H, then G acts as the fundamental group of a graph of groups.
Showed that all vertex and edge groups in this structure are commensurable to H.
Explored the behavior of commensurated subgroups in the context of one-relator groups.

Abstract

We show that if H is a commensurated subgroup of G such that both H and G are of type V F P and vcd ( G ) = vcd ( H ) + 1 , then G is the fundamental group of a graph of groups in which all vertex and edge groups are commensurable to H . We also investigate commensurated subgroups of one-relator groups and duality groups.

问 AI

Bookmark

View Full Paper

问 AI

Bookmark

View Full Paper

Groups of cohomological codimension one

Key Points

Abstract

Cite This Study

Also Consider

Also Consider