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Algebras and Representation Theory

, Volume 21, Issue 2, pp 309–329 | Cite as

The Krull-Schmidt Theorem Holds for Finite Direct Products of Biuniform Groups

  • Alberto Facchini
  • Andrea Lucchini
Article

Abstract

We prove that the Krull-Schmidt Theorem holds for finite direct products of biuniform groups, that is, groups G whose lattice of normal subgroups \(\mathcal {N}(G)\) has Goldie dimension and dual Goldie dimension 1. More generally, it holds for the class of completely indecomposable groups.

Keywords

Lattice of normal subgroups Krull-Schmidt Theorem Normal homomorphism 

Mathematics Subject Classification (2010)

20E15 

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Notes

Acknowledgments

We are grateful to the referee for a careful reading of the previous versions of the paper.

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© Springer Science+Business Media B.V. 2017

Authors and Affiliations

  1. 1.Dipartimento di MatematicaPadovaItaly

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