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

Abstract

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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

How to cite

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Hiroyuki 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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