Displaying similar documents to “Equivalent Expressions of Direct Sum Decomposition of Groups1”

Definition and Properties of Direct Sum Decomposition of Groups1

Kazuhisa Nakasho, Hiroshi Yamazaki, Hiroyuki Okazaki, Yasunari Shidama (2015)

Formalized Mathematics

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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...

Conservation Rules of Direct Sum Decomposition of Groups

Kazuhisa Nakasho, Hiroshi Yamazaki, Hiroyuki Okazaki, Yasunari Shidama (2016)

Formalized Mathematics

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In this article, conservation rules of the direct sum decomposition of groups are mainly discussed. In the first section, we prepare miscellaneous definitions and theorems for further formalization in Mizar [5]. In the next three sections, we formalized the fact that the property of direct sum decomposition is preserved against the substitutions of the subscript set, flattening of direct sum, and layering of direct sum, respectively. We referred to [14], [13] [6] and [11] in the formalization. ...

Decompositions of local rigid ACD groups

Adolf Mader, Otto Mutzbauer (2001)

Colloquium Mathematicae

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We study direct decompositions of extensions of rigid completely decomposable groups by finite primary groups. These decompositions are unique and can be found by finite procedures. By passing to certain quotients the determination of the direct decompositions is made more efficient.

Butler groups splitting over a base element

Clorinda De Vivo, Claudia Metelli (2007)

Colloquium Mathematicae

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We characterize a particular kind of decomposition of a Butler group that is the general case for Butler B(1)-groups; and exhibit a decomposition of a B(2)-group which is not of that kind.

Direct decompositions of uniform groups

A. Mader, O. Mutzbauer (2001)

Colloquium Mathematicae

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Uniform groups are extensions of rigid completely decomposable groups by a finite direct sum of cyclic primary groups all of the same order. The direct decompositions of uniform groups are completely determined by an algorithm that is realised by a MAPLE procedure.