Group with operators: Difference between revisions

Revision as of 13:09, 5 March 2006

Revision as of 14:16, 5 March 2006

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A '''group with operators''' <math>(G, \Omega)</math> is a group <math>G</math> together with a family of [[function (mathematics)|function]]s <math>\Omega</math>

:<math>\omega : G \to G \quad \omega \in \Omega</math>

which are [[distributive]] with respect to the [[group operation]]. The elements of <math>\Omega</math> is called '''operator ___domain''' and its elements are called '''homotheties''' of <math>G</math>.

We denote the image of a group element <math>g</math> under a function <math>\omega</math> with <math>g^\omega</math>. The distributivity can then be expresses as