Find AutZ5SolutionSince Z5 has four generators there are fou

Find Aut(Z5).

Solution

Since Z5 has

four generators, there are four possibilities of assigning a generator as a value to phi(1): (it is the symbol phi)

Phi1(1) = 1; phi2(1) = 2; phi3(1) = 3 and phi4(1) = 4:

Therefore the group Aut(Z5) has four elements. Now we know that a group of order

4 is either isomorphic to the cyclic group Z4 (in which there are elements of order 4)

or to the Klein-group V (in which every element has order 2).