Construction of Finite Loops of Even Order
Using a construction method of , 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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- BRÜck, R. H., A survey of binary systems. Springer-Verlag, Berlin 1958.Google Scholar
- Chein, O., Pflugfelder, H. O., Smith, J. D. H., Quasigroups and Loops, Theory and Applications. Heldermann Verlag, Berlin 1990.Google Scholar
- Kist, G., Theorie der verallgemeinerten kinematischen Räume. Beiträge zur Geometrie und Algebra 14, TUM-Bericht M 8611, München 1986.Google Scholar
- Kreuzer, A. and Wefelscheid, H., On K-loops of fínite order. Res. Math. 25 (1994).Google Scholar