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abelian group

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Definitions of abelian group in various dictionaries:

noun - a group that satisfies the commutative law

ABELIAN GROUP - In abstract algebra, an abelian group, also called a commutative group, is a group in which the result of applying the group operation to two group e...

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Abelian group might refer to
In abstract algebra, an Abelian group, also called a commutative group, is a group in which the result of applying the group operation to two group elements does not depend on the order in which they are written. That is, these are the groups that obey the axiom of commutativity. Abelian groups generalize the arithmetic of addition of integers. They are named after early 19th century mathematician Niels Henrik Abel.The concept of an abelian group is one of the first concepts encountered in undergraduate abstract algebra, from which many other basic concepts, such as modules and vector spaces, are developed. The theory of abelian groups is generally simpler than that of their non-abelian counterparts, and finite abelian groups are very well understood. On the other hand, the theory of infinite abelian groups is an area of current research.
Anagrammer Crossword Solver is a powerful crossword puzzle resource site. We maintain millions of regularly updated crossword solutions, clues and answers of almost every popular crossword puzzle and word game out there. We encourage you to bookmark our puzzle solver as well as the other word solvers throughout our site. Explore deeper into our site and you will find many educational tools, flash cards and plenty more resources that will make you a much better player. Abelian group: In abstract algebra, an abelian group, also called a commutative group, is a group in which the resu...