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WordNet-Online
Definitions from WordNet
Noun abelian group has 1 sense
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Definitions from the WebAbelian GroupDescriptionAn Abelian group is a mathematical concept in the field of abstract algebra. It is a set together with an operation that satisfies the commutative property, meaning that the order of the elements in the operation does not affect the result. In other words, the elements can be added or multiplied in any order. SensesSense 1: Abstract AlgebraIn abstract algebra, an Abelian group, also known as a commutative group, is a set equipped with an operation that is both associative and commutative. The operation usually denoted as addition or multiplication. Example sentence: The integers under addition form an Abelian group since the sum of any two integers is always commutative. Sense 2: MathematicsIn mathematics, an Abelian group refers to a set with a binary operation that satisfies the commutative property. Example sentence: The Abelian group of invertible matrices under multiplication is widely studied in linear algebra. UsagesUsage 1: PopularPopularly, Abelian groups have significant applications in various fields of physics including quantum mechanics and symmetry. Example sentence: Abelian groups are commonly used in quantum field theory to analyze particle interactions and gauge symmetries. Related products: Group Theory in Physics Books on Amazon Usage 2: LocalIn local mathematics communities, Abelian groups are extensively studied in undergraduate courses and research projects. Example sentence: The local math club organized a seminar on the classification of finitely generated Abelian groups. Related products: Abstract Algebra Textbooks on Amazon Note: The links provided are suggestions for related products and can be adapted based on actual availability on Amazon. | ||||
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