The Main Decomposition of Finite-Dimensional Protori

TL;DR

This paper generalizes the decomposition of finite-dimensional protorus into a product of a torus and a complementary factor using duality and torsion-free groups, and classifies certain solenoids.

Contribution

It introduces a broader decomposition framework for finite-dimensional protorus and classifies Hewitt-Ross solenoids by types, extending existing theories.

Findings

Generalized the factorization of protorus using duality.

Classified Hewitt-Ross solenoids by types.

Connected torsion-free groups with protorus decomposition.

Abstract

A protorus is a compact connected abelian group. We use a result on finite rank torsion-free abelian groups and Pontryagin Duality to considerably generalize a well-known factorization of a finite-dimensional protorus into a product of a torus and a torus-free complementary factor. We also classify by types the solenoids of Hewitt and Ross.