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In mathematics and abstract algebra, group theory studies the algebraic structures known as groups.The concept of a group is central to abstract algebra: other well-known algebraic structures, such as rings, fields, and vector spaces, can all be seen as groups endowed with additional operations and axioms.
Gruppentheorie und Quantenmechanik, or The Theory of Groups and Quantum Mechanics, is a textbook written by Hermann Weyl about the mathematical study of symmetry, group theory, and how to apply it to quantum physics.
Examples of the use of groups in physics include the Standard Model, gauge theory, the Lorentz group, and the Poincaré group. Group theory can be used to resolve the incompleteness of the statistical interpretations of mechanics developed by Willard Gibbs , relating to the summing of an infinite number of probabilities to yield a meaningful ...
In group theory, the induced representation is a representation of a group, G, which is constructed using a known representation of a subgroup H.Given a representation of H, the induced representation is, in a sense, the "most general" representation of G that extends the given one.
I: Mon→Grp is the functor sending every monoid to the submonoid of invertible elements and K: Mon→Grp the functor sending every monoid to the Grothendieck group of that monoid. The forgetful functor U: Grp → Set has a left adjoint given by the composite KF: Set → Mon → Grp , where F is the free functor ; this functor assigns to every ...
In group theory, local analysis was started by the Sylow theorems, which contain significant information about the structure of a finite group G for each prime number p dividing the order of G. This area of study was enormously developed in the quest for the classification of finite simple groups , starting with the Feit–Thompson theorem that ...
Group threat theory, also known as group position theory, [1] is a sociological theory that proposes the larger the size of an outgroup, the more the corresponding ingroup perceives it to threaten its own interests, resulting in the ingroup members having more negative attitudes toward the outgroup. [2]
Complement (group theory) Complex reflection group; Component (group theory) Conjugacy class; Conjugacy class sum; Conjugacy problem; Conjugation of isometries in Euclidean space; Convergence group; Core (group theory) Coset; Cosocle; Coxeter complex; Coxeter notation; Cremona group; Crystallographic restriction theorem; Curie's principle ...