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I hope that this is clear. |
If you follow the link family (mathematics) you will see why set (mathematics) is much better. There is no reason to use "family." I am not even sure if anything but sets are used for this theory, so it seems safest to say "set." |
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In [[abstract algebra]], a branch of pure [[mathematics]], the [[algebraic structure]] '''group with operators''' or Ω-'''group''' is a [[group (mathematics)|group]] with a [[
Groups with operators were extensively studied by [[Emmy Noether]] and her school in the 1920s. She employed the concept in her original formulation of the three [[Noether isomorphism theorem]]s.
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For each <math>\omega \in \Omega </math>, the application
:<math>\ g \mapsto g^{\omega}</math>
is then an endomorphism of ''G''. From this, it results that a Ω-group can also be viewed as a group ''G'' with
<math>\Omega</math> is called the '''operator ___domain'''. The associate [[endomorphisms]]{{sfn|Bourbaki|1974|pp=30-31}} are called the '''homotheties''' of ''G''.
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