Finitary permutation groups

In this thesis work we have studied the paper written by A.O. Asar titled `On Finitary Permutation Groups?.In this paper some sufficient conditions are given under which the structure of a transitive group of finitary permutations on an infinite set can be determined from the structure of a point stabilizer. Also, some sufficient conditions are given for the existence of a proper subgroup having an infinite orbit in a totally imprimitive p-group of finitary permutations. These results, with the help of some known results, give sufficient conditions for the nonexistence of a perfect locally finite minimal non FC- (p-group). Thus we made clear and more detailed and put in more easily understandable in this paper.