On t-extensions of abelian groups

TL;DR

This paper introduces t-extensions of abelian groups, showing they form a subgroup of Ext and using them to characterize LCA groups with trivial Pext for all compact connected groups.

Contribution

It defines t-extensions of abelian groups and demonstrates their subgroup structure within Ext, extending previous results on Ext and Pext vanishing conditions.

Findings

t-extensions form a subgroup of Ext(C,G)

Characterization of LCA groups with Pext(C,G)=0

Extension of known results on Ext and Pext

Abstract

Let G and C be two discrete abelian groups. It is known that Pext(C,G) is a subgroup of Ext(C,G). In this paper, we introduce the t-extensions of G by C. We will show that the set of all t-extensions of G by C is a subgroup of Ext(C,G) which contains Pext(C,G). Fulp and Griffith [4] determined the LCA groups G such that Ext(C,G)=0 for all compact connected groups C. Using the group of t-extensions, we determine the LCA groups G such that Pext(C,G)=0 for all compact connected groups C.