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Journal of Automated Reasoning

, Volume 9, Issue 3, pp 291–308 | Cite as

Single axioms for groups

  • Kenneth Kunen
Article

Abstract

We study equations of the form (α=x) which are single axioms for group theory. Earlier examples of such were found by Neumann and McCune. We prove some lower bounds on the complexity of these α, showing that McCune's examples are the shortest possible. We also show that no such α can have only two distinct variables. We do produce an α with only three distinct variables, refuting a conjecture of Neumann. Automated reasoning techniques are used both positively (searching for and verifying single axioms) and negatively (proving that various candidate (α=x) hold in some nongroup and are, hence, not single axioms).

Key words

Group model paramodulation 

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References

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    McCune, W. W., ‘OTTER 2.0 users guide’, Technical Report ANL-90/9, Argonne National Laboratory, 1990.Google Scholar
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    McCune, W. W., ‘What's new in OTTER 2.2’, Technical Memo ANL/MCS-TM-153, Mathematics and Computer Science Division, Argonne National Laboratory, 1991.Google Scholar
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    McCune, W.W., ‘Single axioms for groups and Albelian groups with various operations’, Preprint MCS-P270-1091, Mathematics and Computer Science Division, Argonne National Laboratory, 1991.Google Scholar
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    NeumannB. H., ‘Another single law for groups’, Bull. Australian Math. Soc. 23, 81–102, 1981.Google Scholar
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    NeumannB. H., ‘Yet another single law for groups’, Illinois J. Math. 30, 295–300, 1986.Google Scholar
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Copyright information

© Kluwer Academic Publishers 1992

Authors and Affiliations

  • Kenneth Kunen
    • 1
  1. 1.Computer Sciences DepartmentUniversity of WisconsinMadisonUSA

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