Product Information
Description
An annual survey of the math.GR arXiv category, covering research published from September 2025 – August 2026. Built on a close-reading set of 108 papers and organised into 40 chapters, it maps the year by the field's research sub-directions.
Book framework (share of the year's output):
- Lie Theory, Infinite Groups, and Algebraic Structures (88.2%) — Investigates structural properties of infinite, Lie, and algebraic groups, including contractions, rigidity, and Diophantine problems.
- Subgroup Structure and Finite Group Classification (4.3%) — Focuses on the classification, conjugacy, and structural properties of subgroups within finite and algebraic groups.
- Cayley Graphs, Random Walks, and Group Actions (4.0%) — Studies group actions on graphs, random walks on Cayley graphs, and spectral properties related to growth and orbits.
- Geometric Group Theory and Hyperbolic Spaces (1.4%) — Explores geometric properties of groups, including hyperbolic spaces, quasi-isometries, and fundamental groups of manifolds.
- Representations, Growth, and Invariant Functions (0.9%) — Analyzes linear representations, polynomial growth, and invariant functions within group theory contexts.
- Conjectures and Theorems in Group Theory (0.7%) — Addresses specific open conjectures and proves theorems regarding Artin groups, tensor products, and group laws.
- Open Problems and Counterexamples in Group Theory (0.3%) — Provides solutions, counterexamples, and discussions for open problems listed in the Kourovka Notebook and related literature.
- Set-Theoretic Concepts in Finite Groups (0.1%) — Examines set-based concepts such as Chowla sets, Lagrange subsets, and well-covered graphs within finite groups.
- Sequence Distortion and Representation Theory (0.1%) — Investigates sequence distortion in metric spaces and representation-theoretic conjectures for symmetric and alternating groups.
Each sub-direction is covered across three chapters — how it framed its questions, the strength of its key findings, and its open debates and frontiers — so the reader gets a traceable picture of what this part of the field actually produced over the year.
