Materials Used In Construction And Repair Of Watches

Materials Used In Construction And Repair Of Watches:



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Direct product of groups - Wikipedia

Direct product of groups - Wikipedia: "This operation is the group-theoretic analogue of the Cartesian product of sets and is one of several important notions of direct product in mathematics.
In the context of abelian groups, the direct product is sometimes referred to as the direct sum, and is denoted G ⊕ H. "



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Group theory - Wikipedia

Group theory - Wikipedia: "The first class of groups to undergo a systematic study was permutation groups. Given any set X and a collection G of bijections of X into itself (known as permutations) that is closed under compositions and inverses, G is a group acting on X. If X consists of n elements and G consists of all permutations, G is the symmetric group Sn; in general, any permutation group G is a subgroup of the symmetric group of X. An early construction due to Cayley exhibited any group as a permutation group, acting on itself (X = G) by means of the left regular representation.
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Pullback (differential geometry) - Wikipedia

Pullback (differential geometry) - Wikipedia: "When the map φ is a diffeomorphism, then the pullback, together with the pushforward, can be used to transform any tensor field from N to M or vice versa. In particular, if φ is a diffeomorphism between open subsets of Rn and Rn, viewed as a change of coordinates (perhaps between different charts on a manifold M), then the pullback and pushforward describe the transformation properties of covariant and contravariant tensors used in more traditional (coordinate dependent) approaches to the subject.
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Algebra over a field - Wikipedia

Algebra over a field - Wikipedia: "In mathematics, an algebra over a field (often simply called an algebra), is a vector space equipped with a bilinear product"



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Symplectic group - Wikipedia

Symplectic group - Wikipedia: "The name "symplectic group" is due to Hermann Weyl (details) as a replacement for the previous confusing names of (line) complex group and Abelian linear group, and is the Greek analog of "complex"."



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Group (mathematics) - Wikipedia

Group (mathematics) - Wikipedia: "Many number systems, such as the integers and the rationals enjoy a naturally given group structure. In some cases, such as with the rationals, both addition and multiplication operations give rise to group structures. Such number systems are predecessors to more general algebraic structures known as rings and fields. Further abstract algebraic concepts such as modules, vector spaces and algebras also form groups.
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