Question

Difference between trivial and nontrivial homomorphism

Answer 1

Answer:

trivial Homomorphism

Suppose are finite groups such that their orders are relatively prime. Then, the only homomorphism between and is the trivial map: the map sending every element of to the identity element of .

NONTIVAL HOMOMORPHIN

A subgroup of a group is a normal subgroup having no nontrivial homomorphism to its quotient group if is a normal subgroup of and there is no nontrivial homomorphism from to its quotient group

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