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* Given any group ''G'', (''G'', ∅) is trivially a group with operators
* Given an ''R''-[[module (mathematics)|module]] ''M'', the group ''R'' operates on the operator ___domain ''M'' by [[scalar multiplication]]. More concretely, every [[vector space]] is a group with operators.
==Applications==
The [[Jordan-Holder theorem]] also holds in the context of operator groups. The requirement that a group have a [[composition series]] is analagous to that of [[compact space|compactness]] in [[topology]], and can sometimes be too strong a requirement. It is natural to talk about "compactness relative to a set", i.e. talk about [[composition series]] where each (normal) subgroup is an operator-subgroup relative to the operator set ''X'', of the group in question.
==See also==
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