# Automorphisms of cyclic groups

• Mar 21st 2010, 03:01 AM
sashikanth
Automorphisms of cyclic groups
Prove that a cyclic group of order p (p is prime) has p-1 unique automorphisms.
• Mar 21st 2010, 10:11 AM
Bruno J.
Prove that the group has $p-1$ generators, that an automorphism is uniquely determined by the image of a generator, and that an automorphism must map a generator to a generator.