group of isometry

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• Isometry — For the mechanical engineering and architecture usage, see isometric projection. For isometry in differential geometry, see isometry (Riemannian geometry). In mathematics, an isometry is a distance preserving map between metric spaces. Geometric… …   Wikipedia

• Group theory — is a mathematical discipline, the part of abstract algebra that studies the algebraic structures known as groups. The development of group theory sprang from three main sources: number theory, theory of algebraic equations, and geometry. The… …   Wikipedia

• Isometry group — In mathematics, the isometry group of a metric space is the set of all isometries from the metric space onto itself, with the function composition as group operation. Its identity element is the identity function.A single isometry group of a… …   Wikipedia

• Lorentz group — Group theory Group theory …   Wikipedia

• Euclidean plane isometry — In geometry, a Euclidean plane isometry is an isometry of the Euclidean plane, or more informally, a way of transforming the plane that preserves geometrical properties such as length. There are four types: translations, rotations, reflections,… …   Wikipedia

• Euclidean group — In mathematics, the Euclidean group E ( n ), sometimes called ISO( n ) or similar, is the symmetry group of n dimensional Euclidean space. Its elements, the isometries associated with the Euclidean metric, are called Euclidean moves.These groups… …   Wikipedia

• Symmetry group — Not to be confused with Symmetric group. This article is about the abstract algebraic structures. For other meanings, see Symmetry group (disambiguation). A tetrahedron can be placed in 12 distinct positions by rotation alone. These are… …   Wikipedia

• Fixed points of isometry groups in Euclidean space — A fixed point of an isometry group is a point that is a fixed point for every isometry in the group. For any isometry group in Euclidean space the set of fixed points is either empty or an affine space.For an object, any unique center and, more… …   Wikipedia

• Geometric group theory — is an area in mathematics devoted to the study of finitely generated groups via exploring the connections between algebraic properties of such groups and topological and geometric properties of spaces on which these groups act (that is, when the… …   Wikipedia

• Discrete group — Concepts in group theory category of groups subgroups, normal subgroups group homomorphisms, kernel, image, quotient direct product, direct sum semidirect product, wreath product …   Wikipedia

• Dade isometry — In mathematical finite group theory, the Dade isometry is an isometry from class functions on a subgroup H with support on a subset K of H to class functions on a group G (Collins 1990, 6.1). It was introduced by Dade (1964) as a generalization… …   Wikipedia