Group with operators: Difference between revisions

Revision as of 21:27, 29 August 2006

Revision as of 21:46, 13 September 2006

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== Definition ==

A '''group with operators''' (''G'', ωΩ) is a group ''G'' together with a family of [[function (mathematics)|function]]s Ω:

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

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