On Finitary Permutation Groups

Authors: ALİ OSMAN ASAR

Abstract: In this work we give some sufficient conditions 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, we give some sufficient conditions 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).

Keywords: Finitary permutation, primitive, almost primitive, totally imprimitive

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