# Automorphism, Abelian Group and GCD

Let G be a finite Abelian group of order n, and let m be a positive integer with gcd(m,n)=1. Prove that &#966;:G-->G defined by &#966;(g)=g^m for all g an element of G belongs to Aut(G).

Solution Summary

Automorphism, Abelian Group and GCD are investigated. The solution is detailed and well presented. The response received a rating of "5" from the student who originally posted the question.

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Yupei Xiong, PhD

Rating 4.8/5

Active since 1969

BSc, Peking University
MA, Peking University
PhD, University of Maryland - College Park Campus

Responses 4195

Comments on Yupei's work:

"Thank you very much Dr. Xiong, you really help me a lot. If you have a time, would you please also look at #566852, thank you again for your time and help!"

"the postfix expression must be like this: 1 2 + 3 4 - * 1 2 + / and theres some error Exception in thread "main" java.lang.NumberFormatException: For input string: "3 – 4" at sun.misc.FloatingDecimal.readJavaFormatString(Unknown Source) at java.lang.Double.parseDouble(Unknown Source) at Node.calculate(Node.java:33) at Node.calculate(Node.java:31) at Node.calculate(Node.java:28) at TreeTest.main(TreeTest.java:13)"

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"Thank you for the explanations. I have a better understanding of these problems and how to solve them"

"Thank you! u=sqrt(x) >0 was really a great reasoning. Thanks!"