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.
@article{bwmeta1.element.doi-10_2478_v10037-012-0038-5,
author = {Kenichi Arai and Hiroyuki Okazaki and Yasunari Shidama},
title = {Isomorphisms of Direct Products of Finite Cyclic Groups},
journal = {Formalized Mathematics},
volume = {20},
year = {2012},
pages = {343-347},
zbl = {1277.20067},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_v10037-012-0038-5}
}
Kenichi Arai; Hiroyuki Okazaki; Yasunari Shidama. Isomorphisms of Direct Products of Finite Cyclic Groups. Formalized Mathematics, Tome 20 (2012) pp. 343-347. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_v10037-012-0038-5/
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