Equivalent Expressions of Direct Sum Decomposition of Groups1

Kazuhisa Nakasho; Hiroyuki Okazaki; Hiroshi Yamazaki; Yasunari Shidama

Formalized Mathematics (2015)

  • Volume: 23, Issue: 1, page 67-73
  • ISSN: 1426-2630

Abstract

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In this article, the equivalent expressions of the direct sum decomposition of groups are mainly discussed. In the first section, we formalize the fact that the internal direct sum decomposition can be defined as normal subgroups and some of their properties. In the second section, we formalize an equivalent form of internal direct sum of commutative groups. In the last section, we formalize that the external direct sum leads an internal direct sum. We referred to [19], [18] [8] and [14] in the formalization.

How to cite

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Kazuhisa Nakasho, et al. "Equivalent Expressions of Direct Sum Decomposition of Groups1." Formalized Mathematics 23.1 (2015): 67-73. <http://eudml.org/doc/270901>.

@article{KazuhisaNakasho2015,
abstract = {In this article, the equivalent expressions of the direct sum decomposition of groups are mainly discussed. In the first section, we formalize the fact that the internal direct sum decomposition can be defined as normal subgroups and some of their properties. In the second section, we formalize an equivalent form of internal direct sum of commutative groups. In the last section, we formalize that the external direct sum leads an internal direct sum. We referred to [19], [18] [8] and [14] in the formalization.},
author = {Kazuhisa Nakasho, Hiroyuki Okazaki, Hiroshi Yamazaki, Yasunari Shidama},
journal = {Formalized Mathematics},
keywords = {group theory; direct sum decomposition; direct sums of groups; direct sum decompositions},
language = {eng},
number = {1},
pages = {67-73},
title = {Equivalent Expressions of Direct Sum Decomposition of Groups1},
url = {http://eudml.org/doc/270901},
volume = {23},
year = {2015},
}

TY - JOUR
AU - Kazuhisa Nakasho
AU - Hiroyuki Okazaki
AU - Hiroshi Yamazaki
AU - Yasunari Shidama
TI - Equivalent Expressions of Direct Sum Decomposition of Groups1
JO - Formalized Mathematics
PY - 2015
VL - 23
IS - 1
SP - 67
EP - 73
AB - In this article, the equivalent expressions of the direct sum decomposition of groups are mainly discussed. In the first section, we formalize the fact that the internal direct sum decomposition can be defined as normal subgroups and some of their properties. In the second section, we formalize an equivalent form of internal direct sum of commutative groups. In the last section, we formalize that the external direct sum leads an internal direct sum. We referred to [19], [18] [8] and [14] in the formalization.
LA - eng
KW - group theory; direct sum decomposition; direct sums of groups; direct sum decompositions
UR - http://eudml.org/doc/270901
ER -

References

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