Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Single axioms for odd exponent groups

  • 27 Accesses

  • 14 Citations


With the aid of automated reasoning techniques, we show that all previously known short single axioms for odd exponent groups are special cases of one general schema. We also demonstrate how to convert the proofs generated by an automated reasoning system into proofs understandable by a human.

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


  1. 1.

    Beth, T., Jungnickel, D., and Lenz, H.:Design Theory, Bibliographisches Institut, 1985.

  2. 2.

    Kunen, K.: Single axioms for groups,J. Automated Reasoning 9 (1992), 291–308.

  3. 3.

    Kunen, K.: The shortest single axioms for groups of exponent 4, Technical Report UW#1134, University of Wisconsin, 1993;Computers and Mathematics with Applications 29 (1995), 1–12.

  4. 4.

    McCune, W. W.: OTTER 3.0 reference manual and guide, Technical Report ANL-94/6, Argonne National Laboratory, 1994.

  5. 5.

    McCune, W. W.: Single axioms for groups and Abelian groups with various operations,J. Automated Reasoning 10 (1993), 1–13.

  6. 6.

    McCune, W. W. and Wos. L.: Applications of automated deduction to the search for single axioms for exponent groups, inLogic Programming and Automated Reasoning, Springer-Verlag, 1992, pp. 131–136.

  7. 7.

    Neumann, B. H.: Another single law for groups,Bull. Australian Math. Soc. 23 (1981), 81–102.

  8. 8.

    Tarski, A.: Equational logic and equational theories of algebras, in H. A. Schmidt, K. Schütte, and H.-J. Thiele (eds),Proc. Logic Colloquium, Hannover, 1966, North-Holland, 1968, pp. 275–288.

Download references

Author information

Additional information

Authors supported by NSF Grant DMS-9100665

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Hart, J., Kunen, K. Single axioms for odd exponent groups. J Autom Reasoning 14, 383–412 (1995). https://doi.org/10.1007/BF00881714

Download citation

Key words

  • single axioms
  • odd exponent group

AMS subject classification

  • 68T15
  • 20A05