Group with operators: Difference between revisions

Revision as of 23:48, 8 November 2008

Revision as of 00:55, 17 November 2008

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

A [[subgroup]] ''S'' of ''G'' is called a '''stable subgroup''', '''<math>\omega</math>-subgroup''' or '''<math>\Omega</math>-invariant subgroup''' if it respects the homotheties, that is

:<math>\forall s \in S, \forall \omega \in \Omega : s^\omega \in S.</math>