Abstract
This paper summarizes the results of an investigation into single axioms for groups, both ordinary and Abelian, with each of following six sets of operations: {product, inverse}, {division}, {double division, identity}, {double division, inverse}, {division, identity}, and {division, inverse}. In all but two of the twelve corresponding theories, we present either the first single axioms known to us or single axioms shorter than those previously known to us. The automated theorem-proving program OTTER was used extensively to construct sets of candidate axioms and to search for and find proofs that given candidate axioms are in fact single axioms.
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This work was supported by the Applied Mathematical Sciences subprogram of the Office of Energy Research, U.S. Department of Energy, under Contract W-31-109-Eng-38.
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McCune, W.W. Single axioms for groups and Abelian groups with various operations. J Autom Reasoning 10, 1–13 (1993). https://doi.org/10.1007/BF00881862
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DOI: https://doi.org/10.1007/BF00881862