2023/08/08 by Atticus Stonestrom, Stonestrom, Atticus
Mathematics · #Advanced Topics in Algebra #Advanced Topology and Set Theory #FOS: Mathematics #Group Theory (math.GR) #Logic (math.LO) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2308.04209
openalex publication_date 2023/08/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let G be a dp-minimal group; we prove some consequences of several different hypotheses on G. First, if G is torsion-free, then it is abelian. Second, if G admits a distal f-generic type, then it is virtually nilpotent; we prove this by equipping the quotient of G by its FC-center in this case with a valued group structure. Finally, if G has the uniform chain condition, for example if G is stable, then G is virtually solvable.