Skip to main content
Log in

Subrekursive Komplexität bei Gruppen

II. Der Einbettungssatz von Higman für entscheidbare Gruppen

Subrecursive complexities on groups

II. Higman's embedding theorem for decidable groups

  • Published:
Acta Informatica Aims and scope Submit manuscript

Summary

Higman's embedding theorem states that every recursively presented (r.p.) group can be embedded in a finitely presented (f.p.) group. We use the results of part I together with an idea of Aanderaa [1] to show that the embedding can be realized preserving the complexity of the word problem of the r.p. group.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Literatur

  1. Aanderaa, S.: A proof of Higman's embedding theorem, using Britton extension of groups. In: Word problems (W.W. Boone, F.B. Cannonito, R. Lyndon, eds.), pp. 1–17. Amsterdam-London: North Holland 1975

    Google Scholar 

  2. Avenhaus, J., Madlener, K.: Subrekursive Komplexität bei Gruppen. I. Gruppen mit vorgeschriebener Komplexität. Acta Informat. 9, 87–104 (1977)

    Google Scholar 

  3. Gatterdam, R.W.: The computability of group constructions II. Bull. Austral. Math. Soc. 8, 27–60 (1973)

    Google Scholar 

  4. Higman, G.: Subgroups of finitely presented groups. Proc. Roy. Soc. London Ser. A 262, 455–475 (1961)

    Google Scholar 

  5. Machtey, M.: On the density of honest subrecursive classes. J. Comput. System Sci. 10, 183–199 (1975)

    Google Scholar 

  6. Mehlhorn, K.: Polynomial and abstract subrecursive classes. J. Comput. System Sci, 12, 147–178 (1976)

    Google Scholar 

  7. Rotman, J.J.: The theory of groups, 2nd ed. Boston: Allyn & Bacon 1973

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Avenhaus, J., Madlener, K. Subrekursive Komplexität bei Gruppen. Acta Informatica 9, 183–193 (1978). https://doi.org/10.1007/BF00289077

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00289077

Navigation