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commutative group::noun | Spocien Dictionary
| Type | Words |
|---|---|
| Synonyms | abelian group |
| Type of | group, mathematical group |
Examples of commutative group
commutative group
In abstract algebra, a field is a ring whose nonzero elements form a commutative group under multiplication.
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More generally, every commutative topological group is also a uniform space.
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However, matrix multiplication is not commutative, therefore this group is nonabelian.
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A non-commutative topological group, however, carries two uniform structures, one left-invariant, the other right-invariant.
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The problem is to determine if a black box group, given by k generators, is commutative.
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If the symmetry group is non-commutative, the gauge theory is referred to as non-abelian, the usual example being the Yang-Mills theory.
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Current theories relating to the symmetric group and symmetric functions, commutative algebra, moduli spaces and the representations of Lie groups are rooted in this area.
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In group and set theory, many algebraic structures are called commutative when certain operands satisfy the commutative property.
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