please don't provied handwritten solution..... 4. Is Aut(Z/8Z) isomorphic to Aut(Z/10Z)? Why?

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4. Is Aut(Z/8Z) isomorphic to Aut(Z/10Z)? Why?

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

please don't provied handwritten solution.....

4. Is Aut(Z/8Z) isomorphic to Aut(Z/10Z)? Why?

Expert Solution

Step 1: Note:

Aut(Z_n) isomorphic to U(n) , where n is a natural number

U(2^r) isomorphic Z₂XZ_2^r-2, wher r>2

U(2) is trivial group

U(pⁿ) isomorphic to Z_pⁿ-p^(n-1) for prime p>2

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