Construction of Finite Loops of Even Order
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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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