The profinite genus of the groups ℤⁿ\rtimes C_p²

2025/11/27 by Marlon Estanislau, Estanislau, Marlon, John MacQuarrie +3
Mathematics · #Advanced Operator Algebra Research #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.2511.22658

openalex publication_date 2025/11/27 · openalex created_date 2025/12/03 · openalex updated_date 2026/08/01

Abstract

A formula is given for the profinite genus of groups of the form ℤⁿ \rtimes C_p², completing the calculation of the size of the genus of semidirect products of the form ℤⁿ \rtimes G where G is a finite p-group of finite integral representation type.

Citations

• Profinite rigidity of crystallographic groups arising from Lie theory
• Profinite rigidity of affine Coxeter groups
• Higman-Thompson groups and profinite properties of right-angled Coxeter groups
• Profinite genus of free products with finite amalgamation
• The profinite completion of accessible groups
• Profinite genus of fundamental groups of compact flat manifolds with the cyclic holonomy group of square-free order
• Profinite genus of fundamental groups of compact flat manifolds with holonomy group of prime order
• Distinguishing crystallographic groups by their finite quotients
• Profinite genus of fundamental groups of torus bundles
• Determining Fuchsian groups by their finite quotients

Related

• Profinite genus of fundamental groups of torus bundles
• Profinite genus of free products with finite amalgamation
• Algebraic properties of profinite groups
• Some aspects of profinite group theory
• The strong profinite genus of a finitely presented group can be infinite