Group with operators: Difference between revisions

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MathMartin (talk | contribs)
moved definition of group with operators from Zassenhaus lemma here
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In [[mathematics]], more specifically in [[abstract algebra]], a '''group with operators''' is a [[group (mathematics)|group]] with a [[set (mathematics)|set]] of group [[endomorphism]]s.
 
== Definition ==
 
A '''group with operators''' or a <math>\Omega</math>-'''group''' is a group ''G'' with set ''&Omega;'' and a function
 
:<math>\Omega\rightarrow\operatorname{End}_{\mathbf{Grp}}(G)</math>,
 
where <math>\mathbf{Grp}</math> is the [[category of groups]] and <math>\operatorname{End}_{\mathbf{Grp}}(G)</math> is the set of group [[endomorphism]]s of <math>G</math>.
 
== Examples ==