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Formalized Mathematics

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Volume 23, Issue 1 (Mar 2015)

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Definition and Properties of Direct Sum Decomposition of Groups1

Kazuhisa Nakasho
  • Shinshu University, Nagano, Japan
/ Hiroshi Yamazaki
  • Shinshu University, Nagano, Japan
/ Hiroyuki Okazaki
  • Shinshu University, Nagano, Japan
/ Yasunari Shidama
  • Shinshu University, Nagano, Japan
Published Online: 2015-03-31 | DOI: https://doi.org/10.2478/forma-2015-0002

Summary

In this article, direct sum decomposition of group is mainly discussed. In the second section, support of element of direct product group is defined and its properties are formalized. It is formalized here that an element of direct product group belongs to its direct sum if and only if support of the element is finite. In the third section, product map and sum map are prepared. In the fourth section, internal and external direct sum are defined. In the last section, an equivalent form of internal direct sum is proved. We referred to [23], [22], [8] and [18] in the formalization.

MSC: 20E34; 03B35

Keywords: group theory; direct sum decomposition

MML: identifier: GROUP_19; version: 8.1.03 5.29.1227

Footnotes

  • 1This work was supported by JSPS KAKENHI 22300285.

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About the article

Received: 2014-12-31

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-2015-0002. 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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