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Formalized Mathematics

(a computer assisted approach)

Editor-in-Chief: Matuszewski, Roman

4 Issues per year


SCImago Journal Rank (SJR) 2015: 0.134
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Open Access
Online
ISSN
1898-9934
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Volume 20, Issue 4 (Dec 2012)

Issues

Isomorphisms of Direct Products of Finite Cyclic Groups

Kenichi Arai
  • Tokyo University of Science, Chiba, Japan
/ Hiroyuki Okazaki
  • Shinshu University, Nagano, Japan
/ Yasunari Shidama
  • Shinshu University, Nagano, Japan
Published Online: 2013-02-02 | DOI: https://doi.org/10.2478/v10037-012-0038-5

Summary

In this article, we formalize that every finite cyclic group is isomorphic to a direct product of finite cyclic groups which orders are relative prime. This theorem is closely related to the Chinese Remainder theorem ([18]) and is a useful lemma to prove the basis theorem for finite abelian groups and the fundamental theorem of finite abelian groups. Moreover, we formalize some facts about the product of a finite sequence of abelian groups.

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About the article

Published Online: 2013-02-02

Published in Print: 2012-12-01


Citation Information: Formalized Mathematics, ISSN (Online) 1898-9934, ISSN (Print) 1426-2630, DOI: https://doi.org/10.2478/v10037-012-0038-5. Export Citation

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