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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.

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter4: More On Groups
Section4.7: Direct Sums (optional)
Problem 23E: Prove that if r and s are relatively prime positive integers, then any cyclic group of order rs is...
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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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