What does group action mean?

Definitions for group action
group action

Here are all the possible meanings and translations of the word group action.

Princeton's WordNet

  1. group actionnoun

    action taken by a group of people

Wiktionary

  1. group actionnoun

    a way of describing symmetries of objects using groups

  2. group actionnoun

    A situation in which a large number of agents take action simultaneously in order to achieve a common goal; their actions are usually coordinated.

Freebase

  1. Group action

    In algebra and geometry, a group action is a description of symmetries of objects using groups. The essential elements of the object are described by a set, and the symmetries of the object are described by the symmetry group of this set, which consists of bijective transformations of the set. In this case, the group is also called a permutation group or transformation group. A group action is an extension to the definition of a symmetry group in which every element of the group "acts" like a bijective transformation of some set, without being identified with that transformation. This allows for a more comprehensive description of the symmetries of an object, such as a polyhedron, by allowing the same group to act on several different sets of features, such as the set of vertices, the set of edges and the set of faces of the polyhedron. If G is a group and X is a set then a group action may be defined as a group homomorphism h from G to the symmetric group of X. The action assigns a permutation of X to each element of the group in such a way that the permutation of X assigned to:

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Numerology

  1. Chaldean Numerology

    The numerical value of group action in Chaldean Numerology is: 2

  2. Pythagorean Numerology

    The numerical value of group action in Pythagorean Numerology is: 4

Images & Illustrations of group action

  1. group actiongroup actiongroup actiongroup actiongroup action


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