On a property of the moebius group
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It is shown that the group of all Moebius transformations (M. T.) contains a subgroup Open image in new window such that every non-involutory M. T. not in Open image in new window can be transformed into each of its conjugates outside the subgroup Open image in new window by a unique element of this subgroup. Hence every non-integral and non-involutory M. T. can be reduced into a normal form by means of a unique element of Open image in new window . Also a subgroup Open image in new window *, can be determined such that elements of Open image in new window * reduce all non-involutory M. T. not in Open image in new window *, into their classical (integral) normal forms. There is also a discussion of the question as to other fields over which the results remain valid.
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