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group theory |
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group theoryIn modern algebra, a system consisting of a set of elements and an operation for combining the elements, which together satisfy certain axioms. These require that the group be closed under the operation (the combination of any two elements produces another element of the group), that it obey the associative law, that it contain an identity element (which, combined with any other element, leaves the latter unchanged), and that each element have an inverse (which combines with an element to produce the identity element). If the group also satisfies the commutative law, it is called a commutative, or abelian, group. The set of integers under addition, where the identity element is 0 and the inverse is the negative of a positive number or vice versa, is an abelian group. See also field theory. |
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| A second, circa 1820, was the discovery of group theory by the young French mathematician Galois. Roberts, a journalist, details how this mathematical prodigy's work on the principles of symmetry and group theory defended "visual mathematics" during the 1940s, when a group known as the Bourbakis asserted geometry's irrelevance. Joining together: Group theory and group skills (7th ed. |
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group theory
