Abstract
The material of the two previous chapters is combined to complete the theory of finitely generated ℤ-modules: the invariant factor decomposition. Torsion submodules and the invariance theorem. Primary decomposition, the partition function p(n) and the number of isomorphism classes of finite abelian groups G, provided the prime factorisation of |G| is known.
The endomorphism ring End G and the automorphism group Aut G of a ℤ-module G. Determination of End G and Aut G in the cases finite elementary abelian G and cyclic G (the latter case relies on elementary but intricate number theory). The relation between the invariant factors of subgroups K and factor groups G/K and those of the parent group G.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2012 Springer-Verlag London Limited
About this chapter
Cite this chapter
Norman, C. (2012). Decomposition of Finitely Generated ℤ-Modules. In: Finitely Generated Abelian Groups and Similarity of Matrices over a Field. Springer Undergraduate Mathematics Series. Springer, London. https://doi.org/10.1007/978-1-4471-2730-7_3
Download citation
DOI: https://doi.org/10.1007/978-1-4471-2730-7_3
Publisher Name: Springer, London
Print ISBN: 978-1-4471-2729-1
Online ISBN: 978-1-4471-2730-7
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)