Beitr\ EMIS ELibM Electronic Journals Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 46, No. 1, pp. 215-239 (2005)

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A characterization of subgroup lattices of finite abelian groups

Christian Herrmann and Géza Takách

B. Bergstraesser, Secretary of AG 14, Dept. of Mathematics, University of Technology (Technische Universitaet), Schlossgartenstr. 7, 64289 Darmstadt, Germany, e-mail: bergstraesser@mathematik.tu-darmstadt.de

Abstract: We characterize the lattices of all subgroups of finite Abelian $p$-groups and, more generally, submodules of finitely generated modules over completely primary uniserial rings. This is based on a complete isomorphism invariant for such lattices.

Keywords: primary Arguesian lattice, completely primary uniserial ring, gluing of lattices.

Classification (MSC2000): 06C05, 16P20

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Electronic version published on: 11 Mar 2005. This page was last modified: 4 May 2006.

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