# Groups : Isomorphism and Homomorphism

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)}?

https://brainmass.com/math/linear-transformation/groups-isomorphism-and-homomorphism-15976

#### Solution Preview

No.

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

#### Solution Summary

A group homomorphism is investigated.

$2.19