Abstract Algebra

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Identifying Isomorphisms of Power Maps

ABSALG-ATHEQG

Consider the set $\mathbb{R}^\times$ of nonzero real numbers under multiplication. Let $n$ be a positive integer.

For which values of $n$ is the map $x\mapsto x^n$ an isomorphism?

A

$n=1$ only

B

$n=1,3$ only

C

$n$ odd

D

$n\in \mathbb{Z}_{>0}$.

E

None of the above.