- #1

RJLiberator

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## Homework Statement

φ is a homomorphism of groups.

φ: ℝ^x -> ℝ^x, where φ(α) = α^4, for all α ∈ ℝ^x. Note that ℝ^x is a group under multiplication.

Describe ker(φ) and Im(φ).

## Homework Equations

## The Attempt at a Solution

This is another one of those problems that has me scratching my head due to the way it is written.

What does ℝ^x mean? A real number exponentiated?

If all it does is take α and map it to α^4, then the kernal is just going to be the same as it would be without the mapping?

The image is just exponentiated 4 times.

er?