Group actions on a set and a group

ABSTRACTMSc. THESISGROUP ACTIONS ON A SET AND A GROUPHAKAN ÖZTÜRKDEPARTMENT OF MATHEMATICSINSTITUTE OF NATURAL AND APPLIED SCIENCESUNIVERSITY OF ÇUKUROVASupervisor :Yrd. Doç. Dr. Gonca AYIKYear :2006, Pages: 118Jury:Prof. Dr. Bilal VATANSEVERYrd.Doç. Dr. Ersin KIRALIn this study we gather some fundamental definitions and theorems aboutgroup theory. Such as homomorphism, subgroups and cosets, permutations groups,dihedral groups, normal subgroups and quotient groups, isomorphisms theorems andautomorphism. Then we give definitions and properties of group actions on a sets.Using these information we give a definition of group action on a groups. So we giverelations between group actions on a sets and action on a groups. Finally, using theprogram GAP we give some application of the contents which is stated in this thesis.Key word: Group Actions, Using GAPII