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Searching for small simple automorphic loops

  • Kenneth W. Johnson (a1), Michael K. Kinyon (a2), Gábor P. Nagy (a3) and Petr Vojtěchovský (a4)

Abstract

A loop is (right) automorphic if all its (right) inner mappings are automorphisms. Using the classification of primitive groups of small degrees, we show that there is no non-associative simple commutative automorphic loop of order less than 212, and no non-associative simple automorphic loop of order less than 2500. We obtain numerous examples of non-associative simple right automorphic loops. We also prove that every automorphic loop has the antiautomorphic inverse property, and that a right automorphic loop is automorphic if and only if its conjugations are automorphisms.

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References

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LMS Journal of Computation and Mathematics
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