Group with operators: Difference between revisions

Revision as of 19:58, 4 March 2006

Revision as of 20:05, 4 March 2006

Line 1:

In [[mathematics]], more specifically in [[abstract algebra]], a '''group with operators''' or Ω-'''group''' is a [[group (mathematics)|group]] with a [[set (mathematics)|set]] of group [[endomorphism]]s.

== Definition ==

A '''group with operators''' oris a group <math>\OmegaG</math>-'''group''' is a group ''G''together with a set ''&<math>\Omega;''</math> 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>. The elements of <math>\Omega</math> are called '''homotheties'''.

== Examples ==