Abstract
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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Kreuzer, A. (1995). Construction of Finite Loops of Even Order. In: Fong, Y., Bell, H.E., Ke, WF., Mason, G., Pilz, G. (eds) Near-Rings and Near-Fields. Mathematics and Its Applications, vol 336. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-0359-6_18
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DOI: https://doi.org/10.1007/978-94-011-0359-6_18
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