<abstract xmlns="http://www.w3.org/1999/xhtml"><p>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.</p></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.

Equivalent Expressions of Direct Sum Decomposition of Groups<xref ref-type="fn" rid="fn1_w2aab2b8b1b1b7b1ab1aaAa"><sup>1</sup></xref>

Formalized Mathematics

This work is licensed under the Creative Commons Attribution-ShareAlike 3.0 License.

Equivalent Expressions of Direct Sum Decomposition of Groups

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...

Equivalent Expressions of Direct Sum Decomposition of Groups¹

Published Online: Mar 31, 2015

Page range: 67 - 73

Received: Feb 26, 2015

DOI: https://doi.org/10.2478/forma-2015-0006

Keywords
group theory, direct sum decomposition

© Kazuhisa Nakasho et al.

This work is licensed under the Creative Commons Attribution-ShareAlike 3.0 License.

Equivalent Expressions of Direct Sum Decomposition of Groups1

Published Online: Mar 31, 2015

Page range: 67 - 73

Received: Feb 26, 2015

DOI: https://doi.org/10.2478/forma-2015-0006

Keywordsgroup theory, direct sum decomposition

© Kazuhisa Nakasho et al.

This work is licensed under the Creative Commons Attribution-ShareAlike 3.0 License.

Equivalent Expressions of Direct Sum Decomposition of Groups¹

Keywords
group theory, direct sum decomposition