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arXiv · 1304.3373

Subgroups which admit extensions of homomorphisms

Simion Breaz·Grigore Călugăreanu·Phill Schultz
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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.

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Simion Breaz, Grigore Călugăreanu, Phill Schultz. 2013-04-11. Subgroups which admit extensions of homomorphisms. https://arxiv.org/abs/1304.3373

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