Let G be an abelian group and m be a positive integer. Then the set mG={mn∣x∈G} and G(m)={x∈G∣mx=0} are subgroups of G. Show that the group of automorphism of a cyclic group of degree four is of order two.

Let G be an abelian group and m be a positive integer. Then the set mG={mn∣x∈G} and G(m)={x∈G∣mx=0} are subgroups of G. Show that the group of automorphism of a cyclic group of degree four is of order two.

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

Let G be an abelian group and m be a positive integer.
Then the set
mG={mn∣x∈G}
and G(m)={x∈G∣mx=0} are subgroups of G.

Show that the group of automorphism of a
cyclic group of degree four is of order two.

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