# Definition and Properties of Direct Sum Decomposition of Groups1

Kazuhisa Nakasho; Hiroshi Yamazaki; Hiroyuki Okazaki; Yasunari Shidama

Formalized Mathematics (2015)

- Volume: 23, Issue: 1, page 15-27
- ISSN: 1426-2630

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topKazuhisa Nakasho, et al. "Definition and Properties of Direct Sum Decomposition of Groups1." Formalized Mathematics 23.1 (2015): 15-27. <http://eudml.org/doc/270933>.

@article{KazuhisaNakasho2015,

abstract = {In this article, direct sum decomposition of group is mainly discussed. In the second section, support of element of direct product group is defined and its properties are formalized. It is formalized here that an element of direct product group belongs to its direct sum if and only if support of the element is finite. In the third section, product map and sum map are prepared. In the fourth section, internal and external direct sum are defined. In the last section, an equivalent form of internal direct sum is proved. We referred to [23], [22], [8] and [18] in the formalization.},

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

journal = {Formalized Mathematics},

keywords = {group theory; direct sum decomposition; direct sums of groups; direct products; direct sum decompositions},

language = {eng},

number = {1},

pages = {15-27},

title = {Definition and Properties of Direct Sum Decomposition of Groups1},

url = {http://eudml.org/doc/270933},

volume = {23},

year = {2015},

}

TY - JOUR

AU - Kazuhisa Nakasho

AU - Hiroshi Yamazaki

AU - Hiroyuki Okazaki

AU - Yasunari Shidama

TI - Definition and Properties of Direct Sum Decomposition of Groups1

JO - Formalized Mathematics

PY - 2015

VL - 23

IS - 1

SP - 15

EP - 27

AB - In this article, direct sum decomposition of group is mainly discussed. In the second section, support of element of direct product group is defined and its properties are formalized. It is formalized here that an element of direct product group belongs to its direct sum if and only if support of the element is finite. In the third section, product map and sum map are prepared. In the fourth section, internal and external direct sum are defined. In the last section, an equivalent form of internal direct sum is proved. We referred to [23], [22], [8] and [18] in the formalization.

LA - eng

KW - group theory; direct sum decomposition; direct sums of groups; direct products; direct sum decompositions

UR - http://eudml.org/doc/270933

ER -

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