On an abstract formulation of a theorem of Sierpinski

TL;DR

This paper generalizes an earlier abstract formulation of Sierpiński's theorem within uncountable commutative groups, broadening its applicability and theoretical scope.

Contribution

It extends previous work by providing a more general theorem that applies to a wider class of uncountable commutative groups.

Findings

Generalized Sierpiński theorem to broader group classes

Enhanced understanding of uncountable commutative groups

Established new connections in abstract algebra

Abstract

In an earlier paper, we gave an abstract formulation of a theorem of Sierpi\'nski in uncountable commutative groups. In this paper, we prove a result which generalizes the earlier formulation.