2)Describe explicitly all homomorphisms
h: C_5 ---> Aut(C_11)
Since 11 is prime number, so Aut(C_11) =~ C_10
I worked out that there are 5 homomorphism for C_5 ---> Aut(C_11). Is that true?
let where let then now can be defined to be any element of the set
3)This question I dont know how to do it.
Show that Aut(C_2*C_2) =~ D_6 ( from cyclic group to dihedral group)
Thank you in advanced for your time
since is one-to-one, can be defined to be any element of the set so there are 3 possibilities for and 2 possibilities for therefore
define the automorphisms by: and then and hence
is not cyclic. now use this fact that if is a prime number, then any group of order is either cyclic or it's isomorphisc to
alternatively, see that and [you need to check that all elements of are distinct.] but we have so: