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Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
Let $(Z,+)$ denote the group of all integers under addition. Then the number of all automorphisms of $(Z,+)$ is
Solution
An automorphism of $(Z,+)$ is completely determined by the image of $1$.
The image of $1$ must be a generator of $Z$.
The generators of $Z$ are:
$1$ and $-1$
So, there are only two automorphisms:
$f(n)=n$
$f(n)=-n$
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