On the profinite rigidity of triangle groups
Martin R. Bridson, D. B. McReynolds, Alan W. Reid, Ryan Spitler
Abstract
We prove that certain Fuchsian triangle groups are profinitely rigid in the absolute sense, that is, each is distinguished from all other finitely generated, residually finite groups by its set of finite quotients. We also develop a method based on character varieties that can be used to distinguish between the profinite completions of certain groups.
Topics & Concepts
MathematicsProfinite groupRigidity (electromagnetism)Finitely-generated abelian groupPure mathematicsGenerating set of a groupSet (abstract data type)CombinatoricsFinite setCharacter (mathematics)Group (periodic table)Discrete mathematicsGeometric and Algebraic TopologyFinite Group Theory ResearchAlgebraic Geometry and Number Theory