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Formalized Mathematics

(a computer assisted approach)

Editor-in-Chief: Matuszewski, Roman

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Volume 23, Issue 1


Definition and Properties of Direct Sum Decomposition of Groups1

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


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


  • 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

Citation Information: Formalized Mathematics, Volume 23, Issue 1, Pages 15–27, ISSN (Online) 1898-9934, DOI: https://doi.org/10.2478/forma-2015-0002.

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

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