Group with operators: Difference between revisions

Revision as of 15:34, 2 November 2012

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<math>\Omega</math> is called the '''operator ___domain'''. The associate [[endomorphisms]]{{sfn|Bourbaki|1974|pp=30-31}} are called the '''homotheties''' of ''G''.

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

:<math>\forall \omega \in \Omega, \forall g,h \in G \quad (gh)^{\omega} = g^{\omega}h^{\omega} .</math>

Given two groups ''G'', ''H'' with same operator ___domain <math>\Omega</math>, a '''homomorphism''' of groups with operators is a group homomorphism ''f'':''G''<math>\to</math>''H'' satisfying