Coleman Automorphism Of Finite Groups

Coleman automorphism began with studied the normalization problem of the group G, which is in the units group U(RG) of group ring RG. In other words, the problem about Coleman automorphisms of finite groups are inner automorphisms is studied. In this thesis, through in depth study of Coleman automorphism about finite groups Discussed the circumstances that expansion of two groups which Coleman automorphisms are inner automorphisms, the Coleman automorphism still is inner automorphism. Firstly, given an example that existing group after the expansion of two groups, but its Coleman automorphism is not inner automorphism. In the third chapter, studied the expansion of simple group by certain groups, and the group’s Coleman automorphisms are inner automorphisms. In the fourth chapter, studied the expansion of minimal normal subgroup by certain groups, and the group’s Coleman automorphisms are inner automorphisms. In the fifth chapter, studied the expansion of nilpotent group by certain groups, and the group’s Coleman automorphisms are inner automorphisms. Finally, the application of projected limit in Coleman automorphism group is studied.