Subgroups which admit extensions of homomorphisms

2013/04/11 by Simion Breaz, Breaz, Simion, Grigore Călugăreanu +3
Mathematics · #Commutative Algebra (math.AC) #FOS: Mathematics #Representation Theory (math.RT) #math.AC #math.RT

paper · pdf · doi:10.48550/arxiv.1304.3373

v2: major revision, the title was changed, the paper was shortened, some results were removed

arxiv created 2013/05/30 · arxiv updated 2013/05/31

Abstract

We classify by numerical invariants the finite subgroups H of a primary abelian group G for which every homomorphism or monomorphism of H into G, or every endomorphism of H, extends to an endomorphism of G. We apply these results to show that for finitely generated subgroups of general abelian groups, the extendibility of monomorphisms implies the extendibility of all homomorphisms.

Related

• Cyclic-quasi-injective for Finite Abelian Groups
• Endomorphisms in short exact sequences
• Extensions of Finite Abelian Groups
• An Endomorphism of a Finitely Generated Residually Finite Group
• Fuchs' problem for endomorphisms of abelian groups