AROUND FIXED POINT AUTOMORPHISM OF FINITE ABELIAN P-GROUP ZPA ÃZPB - Syariati Sani, Roro
Let ???? group and ???? ? ????????????(????). The set of all fixed point of ???? contains some important information. Checco, et al. (2010) introduced a framework to study this fixed point set. Let ????(????, ????) be the function that calculates the number of automorphisms that fixed ???? points on ????. This value of ???? can be used to determine the criteria for a nilpoten or solvable group. On the class of finite abelian groups, any group can be decomposed into uniquely direct product of some finite cyclic ????-group. This research will begin by examining the properties of the fixed point automorphisms, the structure of subgrup and its automorphisms group. Then this research calculates the ???? value on cyclic group ????????? , elementary abelian group ????? ???? and group ????????? × ????????? for any prime number ???? and a positive integer ????, ????, ????, ????.