Endomorphisms of the group of all recursive permutations

We describe all endomorphisms of the group Aut_T ɛ of all recursive permutations. It is proved that the family of these endomorphisms is countable, and that they all are continuous and may be defined by some natural recursive operators. Orbits relative to the image of Aut_Tω prove to be recursive, and there exists a recursive model M such that this image is exactly its recursive automorphism group. There exists a universal endomorphism which contains, in a sense, all endomorphisms of that group. The universal endomorphism is unique with respect to some natural recursive equivalence. Supported by RFFR grant No. 093-01-01525. Translated fromAlgebra i Logika, Vol. 36, No. 1, pp. 54–76, January–February, 1997.