Geodesic
Groups of permutations and ideals of Turing degrees
Algebra i logika, Tome 63 (2024) no. 2, pp. 209-224

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We study degrees and degree spectra of groups $\mathfrak{G}_{\mathrm{I}}$ defined on a set of permutations on the natural numbers $\omega$ whose degrees belong to a Turing ideal $\mathrm{I}$. A necessary condition and a sufficient condition are stated which specify whether an arbitrary Turing degree belongs to the degree spectrum of a group $\mathfrak{G}_{\mathrm{I}}$. Nonprincipal ideals $\mathrm{I}$ for which the group $\mathfrak{G}_{\mathrm{I}}$ has or does not have a degree are exemplified.
Keywords: computable permutation, Turing degree, Turing ideal, degree of permutation group, degree spectrum.
Mots-clés : permutation group 
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     author = {A. S. Morozov and V. G. Puzarenko and M. Kh. Faizrahmanov},
     title = {Groups of permutations and ideals of {Turing} degrees},
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     number = {2},
     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2024_63_2_a4/}
}
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A. S. Morozov; V. G. Puzarenko; M. Kh. Faizrahmanov. Groups of permutations and ideals of Turing degrees. Algebra i logika, Tome 63 (2024) no. 2, pp. 209-224. http://geodesic.mathdoc.fr/item/AL_2024_63_2_a4/