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The higman theorem for En (A) computable groups

Part of the Lecture Notes in Mathematics book series (LNM,volume 319)

AMS 1969 subject classifications

  • Primary 02F47
  • 20F05
  • 20F10
  • Secondary 02F35
  • 20E30
  • Key words and phrases
  • Computable groups
  • group presentation
  • word problem
  • embeddings of groups
  • Higman theorem
  • computable function

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References

  1. F. B. Cannonito, Hierarchies of computable groups and the word problem, Journal of symbolic logic 31 (1966) 376–392.

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. F. B. Cannonito and R. W. Gatterdam, The computability of group constructions, part I, Proceedings of the Irvine conference on decision problems in group theory (North Holland in preparation).

    Google Scholar 

  3. C. R. J. Clapham, Finitely presented groups with word problem of arbitrary degrees of insolubility, Proceedings of the London Mathematical Society 14 (1966) 633–676.

    MathSciNet  MATH  Google Scholar 

  4. C. R. J. Clapham, An embedding theorem for finitely generated groups, Proceedings of the London Mathematical Society 17 (1967) 419–430.

    CrossRef  MathSciNet  MATH  Google Scholar 

  5. R. W. Gatterdam, Embeddings of primitive recursive computable groups, doctoral dissertation, University of California, Irvine, 1970. Submitted to Annals of mathematical logic.

    Google Scholar 

  6. R. W. Gatterdam, The Higman theorem for primitive recursive groups—a preliminary report, Proceedings of the Irvine conference on decision problems in group theory (North Holland in preparation).

    Google Scholar 

  7. R. W. Gatterdam, The computability of group constructions part II, to appear.

    Google Scholar 

  8. A. Grzegorczyk, Some classes of recursive functions, Rozprawy Mathmetyczne 4 (1953) 46 pp.

    Google Scholar 

  9. G. Higman, Subgroups of finitely presented groups, Proceedings of the Royal Society, A 262 (1961) 455–475.

    CrossRef  MathSciNet  MATH  Google Scholar 

  10. M. O. Rabin, Computable algebra, general theory and theory of computable fields, Transactions of the American Mathematical Society 95 (1960) 341–360.

    MathSciNet  MATH  Google Scholar 

  11. R. W. Ritchie, Classes of recursive functions based on Ackerman's function, mimeographed lecture notes, University of Washington, 1963.

    Google Scholar 

  12. J. R. Schoenfield, Mathematical Logic (Addison Wesley 1967).

    Google Scholar 

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© 1973 Springer Verlag

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Gatterdam, R.W. (1973). The higman theorem for En (A) computable groups. In: Gatterdam, R.W., Weston, K.W. (eds) Conference on Group Theory. Lecture Notes in Mathematics, vol 319. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0058930

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  • DOI: https://doi.org/10.1007/BFb0058930

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-06205-9

  • Online ISBN: 978-3-540-38479-3

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