- #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?