Direct sum of groups
In mathematics, a group G is called the direct sum of two normal subgroups with trivial intersection if it is generated by the subgroups. In abstract algebra, this method of construction of groups can be generalized to direct sums of vector spaces, modules, and other structures; see the article direct sum of modules for more information. A group which can be expressed as a direct sum of non-trivial subgroups is called decomposable, and if a group cannot be expressed as such a direct sum then it is called indecomposable.
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Abelian groupAdjoint functorsCentral seriesDe Rham cohomologyDirect productDirect sumDirect sum of topological groupsDuality (mathematics)Finitely generated abelian groupFinitely generated groupFree abelian groupGlossary of group theoryGroup homomorphismGroup representationHomotopy groups of spheresInjective cogeneratorIsomorphism theoremsList of group theory topicsLocally cyclic groupModulatory spacePre-abelian categorySumToda bracketTorsion conjectureTorsion subgroupWeak direct productWreath product
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Direct sum of groups
In mathematics, a group G is called the direct sum of two normal subgroups with trivial intersection if it is generated by the subgroups. In abstract algebra, this method of construction of groups can be generalized to direct sums of vector spaces, modules, and other structures; see the article direct sum of modules for more information. A group which can be expressed as a direct sum of non-trivial subgroups is called decomposable, and if a group cannot be expressed as such a direct sum then it is called indecomposable.
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In mathematics, a group G is c ...... n it is called indecomposable.
@en
在數學中,群 G 叫做子群的集合 {Hi} 的直和,如果
...... = <{Hi}>;換句話說,G 是子群 {Hi} 生成的。
@zh
数学における群の直和(ちょくわ、英: direct sum) ...... A × B と書く代わりに) A ⊕ B で表すことがある。
@ja
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In mathematics, a group G is c ...... n it is called indecomposable.
@en
在數學中,群 G 叫做子群的集合 {Hi} 的直和,如果
...... = <{Hi}>;換句話說,G 是子群 {Hi} 生成的。
@zh
数学における群の直和(ちょくわ、英: direct sum) ...... A × B と書く代わりに) A ⊕ B で表すことがある。
@ja
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Direct sum of groups
@en
群の直和
@ja
群的直和
@zh