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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Turing degrees of nonabelian groups
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by M. A. Dabkowska, M. K. Dabkowski, V. S. Harizanov and A. S. Sikora PDF
Proc. Amer. Math. Soc. 135 (2007), 3383-3391 Request permission

Abstract:

For a countable structure $\mathcal {A}$, the (Turing) degree spectrum of $\mathcal {A}$ is the set of all Turing degrees of its isomorphic copies. If the degree spectrum of $\mathcal {A}$ has the least degree $\mathbf {d}$, then we say that $\mathbf {d}$ is the (Turing) degree of the isomorphism type of $\mathcal {A}$. So far, degrees of the isomorphism types have been studied for abelian and metabelian groups. Here, we focus on highly nonabelian groups. We show that there are various centerless groups whose isomorphism types have arbitrary Turing degrees. We also show that there are various centerless groups whose isomorphism types do not have Turing degrees.
References
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Additional Information
  • M. A. Dabkowska
  • Affiliation: Department of Mathematics, George Washington University, Washington, D.C. 20052
  • Email: gdab@gwu.edu
  • M. K. Dabkowski
  • Affiliation: Department of Mathematical Sciences, University of Texas at Dallas, Richardson, Texas 75083
  • Email: mdab@utdallas.edu
  • V. S. Harizanov
  • Affiliation: Department of Mathematics, George Washington University, Washington, D.C. 20052
  • Email: harizanv@gwu.edu
  • A. S. Sikora
  • Affiliation: Department of Mathematics, State University of New York at Buffalo, Buffalo, New York 14260
  • MR Author ID: 364939
  • Email: asikora@buffalo.edu
  • Received by editor(s): March 21, 2006
  • Received by editor(s) in revised form: July 1, 2006
  • Published electronically: May 14, 2007
  • Communicated by: Julia Knight
  • © Copyright 2007 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 135 (2007), 3383-3391
  • MSC (2000): Primary 03C57, 03D45
  • DOI: https://doi.org/10.1090/S0002-9939-07-08845-4
  • MathSciNet review: 2322771