Abstract
It is proved that an o-2-transitive group of order automorphisms of a totally ordered set with Abelian stabilizer of a point is the permutation groupF={φ(a, b)‖a, bεP, a>0, (x)φ(a, b)=xa+b forxεP} of a totally ordered fieldP.
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References
A. I. Kokorin and V. M. Kopytov,Fully Ordered Groups [in Russian], Nauka, Moscow (1972).
V. M. Kopytov,Lattice-Ordered Groups [in Russian], Nauka, Moscow (1984).
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Translated fromMatematicheskie Zametki, Vol. 65, No. 2, pp. 289–293, February, 1999.
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Tararin, V.M. O-2-transitive automorphism groups with abelian stabilizer of a point. Math Notes 65, 238–241 (1999). https://doi.org/10.1007/BF02679822
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DOI: https://doi.org/10.1007/BF02679822