The Structure Of Automorphism Groups Of Groups Order2~4

The research of the automorphism group of a group is a very important part of group theory, according to the Sylow theorem, we know that the group has Sylow p-subgroups, and because automorphism keep the orders of elements unchanged, so the research of the automorphism group of a group turn into the research of the automor-phism group of a p-group. In this paper, we give the structure of a kind of p-group’s au-tomorphism group, i.e.the structure of automorphism groups of groups order16. First according to the properties of automorphism,I found the order of the automorphism groups, and then find the generating element and calculation of their relationship,and at last I calculate their permutation representations.