Question

If G is a group which Aut(G)={1},prove that |G| is no more than 2

Answer 1

If there are three elements, say the neutral e and two other g and h, then there is the automorphism \[x ↦ gh^{-1}x\] which is non-trivial for \[g\neq h\]

Answer 2

thank you

Answer 3

mmh, just thinking that might not be homomorphic. Better take \[x ↦ gh^{-1}xhg^{-1}\] because then you have \[xy ↦ gh^{-1}xyhg^{-1} = gh^{-1}xhg^{-1}\;gh^{-1}yhg^{-1}\]

Answer 4

yeah ,thanks nowhereman!