Question

number of homomorphism from K4 to S4?
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Answer 1

Step-by-step explanation:

How many homomorphism from S3 to S4? Please find these using fundamental theorem.

I think if f:G→G′ is a group homomorphism then G/kerf is isomorphic to a subgroup of G′. For one choice of kerf, the order of G/kerf is k and G′ has n subgroups of order k . Hence there are n homomorphisms.

But in case of S3 to S4, if S3/kerf is a subgroup of S4 then we have three cases: