Algebraic properties of profinite groups

Abstract

Recently there has been a lot of research and progress in profinite groups. We survey some of the new results and discuss open problems. A central theme is decompositions of finite groups into bounded products of subsets of various kinds which give rise to algebraic properties of topological groups.

This version has some references updated

References in corpus (8)

• Measure Preserving Words are Primitive
• Generators and commutators in finite groups; abstract quotients of compact groups
• Approximate subgroups of linear groups
• Expansion properties of finite simple groups
• Suzuki groups as expanders
• Rank and genus of 3-manifolds
• Presentations of Finite Simple Groups: Profinite and Cohomological Approaches
• Comparison of the Discrete and Continuous Cohomology Groups of a Pro-$p$ Group

Cited by in corpus (5)

• Locally normal subgroups of totally disconnected groups. Part II: Compactly generated simple groups
• Word equations in simple groups and polynomial equations in simple algebras
• On discrete homology of a free pro-$p$-group
• Remarks on profinite groups having few open subgroups
• On small profinite groups