Ok, I think I got it.
Let G be a group generated by x of order 2 and y of order 17.
Let Ic be the inner automorphism defined by Ic(a) = cac^-1, for some c in G, all a in G.
Let Id be the inner automorphism defined by Id(a) = dad^-1, for some d in G, all a in G.
Then cac^-1 = dad^-1 ==>...
Ok, this seems to be coming together.
Let G be a group generated by x of order 2 and y of order 17.
Let Ic be the inner automorphism defined by Ic(a) = cac^-1, for some c in G, all a in G.
Let Id be the inner automorphism defined by Id(a) = dad^-1, for some d in G, all a in G.
Then...
Homework Statement
I need to show that for a group G of order 34 that if the order of the automorphism group is less than or equal to to 33, then G is cyclic.
Homework Equations
none
The Attempt at a Solution
I'm mainly trying to do a proof by contradiction. First I assumed that G...