AROUND FIXED POINT AUTOMORPHISM OF FINITE ABELIAN P-GROUP ZPA ÃZPB
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...
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| Format: | Theses |
| Language: | Indonesia |
| Online Access: | https://digilib.itb.ac.id/gdl/view/55104 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | 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 ????, ????, ????, ????. |
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