# Isomorphisms of Direct Products of Finite Cyclic Groups

Kenichi Arai; Hiroyuki Okazaki; Yasunari Shidama

Formalized Mathematics (2012)

- Volume: 20, Issue: 4, page 343-347
- ISSN: 1426-2630

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topKenichi Arai, Hiroyuki Okazaki, and Yasunari Shidama. "Isomorphisms of Direct Products of Finite Cyclic Groups." Formalized Mathematics 20.4 (2012): 343-347. <http://eudml.org/doc/267547>.

@article{KenichiArai2012,

abstract = {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.},

author = {Kenichi Arai, Hiroyuki Okazaki, Yasunari Shidama},

journal = {Formalized Mathematics},

keywords = {formalized mathematics; finite cyclic groups; finite Abelian groups; direct products},

language = {eng},

number = {4},

pages = {343-347},

title = {Isomorphisms of Direct Products of Finite Cyclic Groups},

url = {http://eudml.org/doc/267547},

volume = {20},

year = {2012},

}

TY - JOUR

AU - Kenichi Arai

AU - Hiroyuki Okazaki

AU - Yasunari Shidama

TI - Isomorphisms of Direct Products of Finite Cyclic Groups

JO - Formalized Mathematics

PY - 2012

VL - 20

IS - 4

SP - 343

EP - 347

AB - 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.

LA - eng

KW - formalized mathematics; finite cyclic groups; finite Abelian groups; direct products

UR - http://eudml.org/doc/267547

ER -

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