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.
@article{bwmeta1.element.doi-10_2478_forma-2015-0006,
author = {Kazuhisa Nakasho and Hiroyuki Okazaki and Hiroshi Yamazaki and Yasunari Shidama},
title = {Equivalent Expressions of Direct Sum Decomposition of Groups1},
journal = {Formalized Mathematics},
volume = {23},
year = {2015},
pages = {67-73},
zbl = {1317.20034},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_forma-2015-0006}
}
Kazuhisa Nakasho; Hiroyuki Okazaki; Hiroshi Yamazaki; Yasunari Shidama. Equivalent Expressions of Direct Sum Decomposition of Groups1. Formalized Mathematics, Tome 23 (2015) pp. 67-73. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_forma-2015-0006/
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