# Isomorphisms of Direct Products of Finite Commutative Groups

Hiroyuki Okazaki; Hiroshi Yamazaki; Yasunari Shidama

Formalized Mathematics (2013)

- Volume: 21, Issue: 1, page 65-74
- ISSN: 1426-2630

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topHiroyuki Okazaki, Hiroshi Yamazaki, and Yasunari Shidama. "Isomorphisms of Direct Products of Finite Commutative Groups." Formalized Mathematics 21.1 (2013): 65-74. <http://eudml.org/doc/267309>.

@article{HiroyukiOkazaki2013,

abstract = {We have been working on the formalization of groups. In [1], we encoded some theorems concerning the product of cyclic groups. In this article, we present the generalized formalization of [1]. First, we show that every finite commutative group which order is composite number is isomorphic to a direct product of finite commutative groups which orders are relatively prime. Next, we describe finite direct products of finite commutative groups},

author = {Hiroyuki Okazaki, Hiroshi Yamazaki, Yasunari Shidama},

journal = {Formalized Mathematics},

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

language = {eng},

number = {1},

pages = {65-74},

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

url = {http://eudml.org/doc/267309},

volume = {21},

year = {2013},

}

TY - JOUR

AU - Hiroyuki Okazaki

AU - Hiroshi Yamazaki

AU - Yasunari Shidama

TI - Isomorphisms of Direct Products of Finite Commutative Groups

JO - Formalized Mathematics

PY - 2013

VL - 21

IS - 1

SP - 65

EP - 74

AB - We have been working on the formalization of groups. In [1], we encoded some theorems concerning the product of cyclic groups. In this article, we present the generalized formalization of [1]. First, we show that every finite commutative group which order is composite number is isomorphic to a direct product of finite commutative groups which orders are relatively prime. Next, we describe finite direct products of finite commutative groups

LA - eng

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

UR - http://eudml.org/doc/267309

ER -

## References

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