# Normal Subgroup of Product of Groups

Hiroyuki Okazaki; Kenichi Arai; Yasunari Shidama

Formalized Mathematics (2011)

- Volume: 19, Issue: 1, page 23-26
- ISSN: 1426-2630

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topHiroyuki Okazaki, Kenichi Arai, and Yasunari Shidama. "Normal Subgroup of Product of Groups." Formalized Mathematics 19.1 (2011): 23-26. <http://eudml.org/doc/266892>.

@article{HiroyukiOkazaki2011,

abstract = {In [6] it was formalized that the direct product of a family of groups gives a new group. In this article, we formalize that for all j ∈ I, the group G = Πi∈IGi has a normal subgroup isomorphic to Gj. Moreover, we show some relations between a family of groups and its direct product.},

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

journal = {Formalized Mathematics},

keywords = {direct products of groups; direct sums; normal subgroups},

language = {eng},

number = {1},

pages = {23-26},

title = {Normal Subgroup of Product of Groups},

url = {http://eudml.org/doc/266892},

volume = {19},

year = {2011},

}

TY - JOUR

AU - Hiroyuki Okazaki

AU - Kenichi Arai

AU - Yasunari Shidama

TI - Normal Subgroup of Product of Groups

JO - Formalized Mathematics

PY - 2011

VL - 19

IS - 1

SP - 23

EP - 26

AB - In [6] it was formalized that the direct product of a family of groups gives a new group. In this article, we formalize that for all j ∈ I, the group G = Πi∈IGi has a normal subgroup isomorphic to Gj. Moreover, we show some relations between a family of groups and its direct product.

LA - eng

KW - direct products of groups; direct sums; normal subgroups

UR - http://eudml.org/doc/266892

ER -

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