Content deleted Content added
alg struct template |
→Definition: Adding definition of homomorphism |
||
Line 12:
We denote the image of a group element ''g'' under a function <math>\omega</math> with <math>g^\omega</math>. The distributivity can then be expressed as
:<math>\forall \omega \in \Omega, \forall g,h \in G \quad (gh)^{\omega} = g^{\omega}h^{\omega} .</math>
Given two groups ''G'', ''H'' with same operator ___domain <math>\Omega</math>, a '''homomorphism''' of groups with operators is a group homomorphism ''f'':''G''<math>\to</math>''H'' satisfying
:<math>\forall \omega \in \Omega, \forall g \in G : f(g^\omega)=(f(g))^\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
| |||