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Formalized Mathematics

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Volume 23, Issue 1 (Mar 2015)

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Equivalent Expressions of Direct Sum Decomposition of Groups1

Kazuhisa Nakasho
  • Shinshu University, Nagano, Japan
/ Hiroyuki Okazaki
  • Shinshu University, Nagano, Japan
/ Hiroshi Yamazaki
  • Shinshu University, Nagano, Japan
/ Yasunari Shidama
  • Shinshu University, Nagano, Japan
Published Online: 2015-03-31 | DOI: https://doi.org/10.2478/forma-2015-0006

Summary

In this article, the equivalent expressions of the direct sum decomposition of groups are mainly discussed. In the first section, we formalize the fact that the internal direct sum decomposition can be defined as normal subgroups and some of their properties. In the second section, we formalize an equivalent form of internal direct sum of commutative groups. In the last section, we formalize that the external direct sum leads an internal direct sum. We referred to [19], [18] [8] and [14] in the formalization.

MSC: 20E34; 03B35

Keywords: group theory; direct sum decomposition

MML: identifier: GROUP _20; version: 8.1.04 5.31.1231

Footnotes

  • 1This work was supported by JSPS KAKENHI 22300285.

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About the article

Received: 2015-02-26

Published Online: 2015-03-31

Published in Print: 2015-03-01


1This work was supported by JSPS KAKENHI 22300285.


Citation Information: Formalized Mathematics, ISSN (Online) 1898-9934, DOI: https://doi.org/10.2478/forma-2015-0006. Export Citation

© Kazuhisa Nakasho et al.. This work is licensed under the Creative Commons Attribution-ShareAlike 3.0 License. (CC BY-SA 3.0)

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