On t-extensions of abelian groups
Hussain Sahleh, Aliakbar Alijani

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.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Rings, Modules, and Algebras · Homotopy and Cohomology in Algebraic Topology
