Assertion: normality | /r/HasProperty | preserved
Facets:
value: on taking direct products
type: OTHER
value: by taking inverse images
type: MANNER
Source sentences:
text: Normality is preserved by taking inverse images, i.e. if G → H is a group homomorphism and N is normal in H , then the inverse image f -1 ( N ) is normal in G .
text: Normality is preserved on taking direct products, i.e. if N 1 ◃ G 1 {\displaystyle N_{1}\triangleleft G_{1}} N 2 ◃ G 2 {\displaystyle N_{2}\triangleleft G_{2}} N 1 × N 2 ◃ G 1