Let G be a finite, Abelian group and let n be a positive integer relatively prime to the order o

Name: Let G be a finite, Abelian group and let n be a positive integer relatively prime to the order of G. Prove that the map ?(a) = a? a ? G is an automorphism of G. Some background: if a map from a finite group to itself is one-to-one, then it is also onto. Proving that this ? is operation-preserving is the easy part of this question.
Uploaded: 2023-10-16T18:13:32-08:00
Duration: 3 min 24 s
Channel: Supreeta N
Description: Let G be a finite, Abelian group and let n be a positive integer relatively prime to the order of G. Prove that the map ?(a) = a? a ? G is an automorphism of G. Some background: if a map from a finite group to itself is one-to-one, then it is also onto. Proving that this ? is operation-preserving is the easy part of this question.

Question

Brent Burkett · Accepted Answer

1. First, we need to show that the map $o$ is well-defined, i.e., if $a in G$, then $a^n in G$

Question

Please give Ace some feedback