Group action  From Wikipedia, the free encyclopedia
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search This article is about the mathematical concept. For the
sociology term, see group action (sociology).  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 (especially if the set is finite
or not a vector space) or transformation group (especially if
the set is a vector space and the group acts like linear
transformations of the set).  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 (or "symmetry") of
some set, without being identified with that transformation.
This allows for a more comprehensive desc