# Groups : Isomorphism and Homomorphism

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Note:

S4 means symmetric group of degree 4

A4 means alternating group of degree 4

e is the identity

Is there a group homomorphism $:S4 -> A4, with

kernel $ = {e, (1 2)(3 4), (1 3)(2 4), (1 4)(2 3)}?

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##### Solution Summary

A group homomorphism is investigated.

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No.

By the isomorphism theory, if there is a group homomorphism $: S4->A4, ...

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