On the total number of principal series of a finite abelian group

In this note we give a bijective proof for the explicit formula giving the total number of principal series of the direct product \(\mathbb{Z}_{p^{\alpha_1}} \times \mathbb{Z}_{p^{\alpha_2}}\), where \(p\) is a prime number. This new proof is easier to generalize to arbitrary finite abelian groups t...

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Bibliographic Details
Published in:arXiv.org 2018-05
Main Authors: Bentea, Lucian, Tărnăuceanu, Marius
Format: Article
Language:English
Subjects:
Group theory
Series (mathematics)
Online Access:Get full text
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Summary:In this note we give a bijective proof for the explicit formula giving the total number of principal series of the direct product \(\mathbb{Z}_{p^{\alpha_1}} \times \mathbb{Z}_{p^{\alpha_2}}\), where \(p\) is a prime number. This new proof is easier to generalize to arbitrary finite abelian groups than the original direct calculation method.
ISSN:2331-8422