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

  • Michael Kinyon
  • Robert Veroff
  • Petr Vojtěchovský
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7788)


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.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Michael Kinyon
    • 1
  • Robert Veroff
    • 2
  • Petr Vojtěchovský
    • 1
  1. 1.Department of MathematicsUniversity of DenverDenverUSA
  2. 2.Department of Computer ScienceUniversity of New MexicoAlbuquerqueUSA

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