Group homomorphism
Group homomorphism In mathematics, given two groups (G, *) and (H, ·), a group homomorphism from (G, *) to (H, ·) is a ... say that h "is compatible with the group structure". Older notations for the homomorphism ...
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Homomorphism of group   (translated from French)
Homomorphism of group A morphism of group (one says also homomorphism of group) is an application of a group ...
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Homomorphism
Homomorphism This word should not be confused with homeomorphism. In abstract algebra, a homomorphism is a structure-preserving map between two ... groups, rings, or vector spaces). The word homomorphism comes from the Greek language: homo meaning ... Note that f(x) = 3x is a homomorphism, since f(a + b) = 3(a + b ... f(a) + f(b). Note that this homomorphism maps the natural numbers back onto ...
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Lie group
Lie group In mathematics, a Lie group is an analytic real or complex manifold that is also a group such that the group operations multiplication and inversion are analytic maps ... space R n is a real Lie group (with ordinary vector addition as the ...
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Group representation
Group representation Group representation theory is the branch of mathematics ... theory is important because it enables many group-theoretic problems to be reduced to problems ... is used to describe how the symmetry group of a physical system affects the solutions ... of groups. The term representation of a group is also used in a more ...
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Group action
Group action This article is about the mathematical concept. For the sociology term, see group action (sociology). In mathematics, a symmetry group describes all symmetries of objects. This is formalized by the notion of a group action: every element of the group "acts" like a bijective map (or " ...
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Lorentz group
Lorentz group In physics, the Lorentz group is the group of all Lorentz transformations of Minkowski spacetime ... invariant under Lorentz transformations. Therefore the Lorentz group can be said to express a fundamental ... laws of nature. Basic properties The Lorentz group is a subgroup of the Poincaré ...
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Fundamental group
Fundamental group In mathematics, the fundamental group is one of the basic concepts of ... a topological space there is a fundamental group that conveys information about the 1-dimensional ... space surrounding the given point. The fundamental group is the first homotopy group. Intuition and definition Before giving a ...
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Ring homomorphism
Ring homomorphism In abstract algebra, a ring homomorphism is a function between two rings which ... and S are rings, then a ring homomorphism is a function f : R → S ... of two ring homomorphisms is a ring homomorphism. It follows that the class of all ... f(a)) −1 . Therefore, f induces a group homomorphism from the group of units ...
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Modular group
Modular group In mathematics, the modular group Γ (Gamma) is a group that is a fundamental object of study ... other areas of advanced mathematics. The modular group can be represented as a group of geometric transformations or as a ...
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