Countably compact groups having minimal infinite powers

TL;DR

This paper investigates whether the infinite power of countably compact minimal Abelian groups remains minimal, revealing that the answer depends on the existence of measurable cardinals, thus linking topology with set theory.

Contribution

It establishes an equivalence between the minimality of infinite powers of certain groups and the existence of measurable cardinals, answering a long-standing open question.

Findings

The power G^omega is minimal if and only if measurable cardinals exist.

The question from over thirty years ago is resolved through set-theoretic assumptions.

The result connects topological group properties with large cardinal axioms.

Abstract

We answer the question, raised more than thirty years ago, on whether the power (G raised to the power omega) of a countably compact minimal Abelian group G is minimal, by showing that the negative answer is equivalent to the existence of measurable cardinals.