Construction of Finite Loops of Even Order

  • Alexander Kreuzer
Part of the Mathematics and Its Applications book series (MAIA, volume 336)


Using a construction method of [9], we give examples of non-associative loops with additional properties. These are power associative, left alternative loops which satisfy the automorphic inverse property and the left inverse property but not the Bol identity. It will be shown that, for n, k ∈ ℕ, non-isomorphic K-loops (L, ⊕) of order 8kn exist which are also Bruck loops, having commutative subgroups (G, ⊕) and (H, ⊕) of order An and 2k, respectively with L = G ⊕ H.


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Copyright information

© Springer Science+Business Media Dordrecht 1995

Authors and Affiliations

  • Alexander Kreuzer
    • 1
  1. 1.Mathematisches InstitutTechnische Universität MünchenMünchenGermany

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