Chapter

Automated Reasoning and Mathematics

Volume 7788 of the series Lecture Notes in Computer Science pp 151-164

Loops with Abelian Inner Mapping Groups: An Application of Automated Deduction

  • Michael KinyonAffiliated withDepartment of Mathematics, University of Denver
  • , Robert VeroffAffiliated withDepartment of Computer Science, University of New Mexico
  • , Petr VojtěchovskýAffiliated withDepartment of Mathematics, University of Denver

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Abstract

We describe a large-scale project in applied automated deduction concerned with the following problem of considerable interest in loop theory: If Q is a loop with commuting inner mappings, does it follow that Q modulo its center is a group and Q modulo its nucleus is an abelian group? This problem has been answered affirmatively in several varieties of loops. The solution usually involves sophisticated techniques of automated deduction, and the resulting derivations are very long, often with no higher-level human proofs available.