Abstract
In this note examples are given for non trivial K-loops. There are commutative examples as well as non commuative, finite examples as well as infinite. Furthermore it will be shown that under an additional condition K-loops and Brück loops coincide.
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Bol, G. Gewebe und Gruppen. Math Ann. 114 (1937), 414–431
Burn, R. P. Finite Bol loops. Math. Proc. Cambridge Philos. Soc. 84 (1978), 377–385
Chein, O., Pflugfelder, H.O., Smith, J. D. H.: Quasigroups and Loops, Theory and Applications. Heldermann Verlag, Berlin 1990
Glauberman, G.: On Loops of Odd Order. J. Algebra 1 (1966), 374–396
Karzel, H.: Zusammenhänge zwischen Fastbereichen, scharf zweifach transitven Permutationsgruppen und 2-Strukturen mit Rechtecksaxiom. Abh. Math Sem. Univ. Hamburg 32 (1968), 191–206
Kist, G.: Theorie der verallgemeinerten kinematischen Räume. Beiträge zur Geometrie und Algebra 14, TUM— Bericht M 8611, München 1986
Niederreiter, H. and Robinson, K. H.: Bol loops of order pq. Math. Proc. Cambridge Philos. Soc. 89 (1981), 241–256
Robinson, D. A.: Bo1-Loops. Trans Amer. Math. Soc. 123 (1966), 341–354
Ungar, A., A.: Thomas rotation and the parametrization of the Lorentz transformation group. Found. Phys. Lett. 1 (1988), 57–89
Ungar, A.,A.: Weakly associative groups. Res. Math. 17(1990), 149–168
WÄhling, H.: Theorie der Fastkörper. Thales Verlag, Essen 1987
Wefelscheid, H.: K-Loops and their use in the theory of special relativity. Preprint
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Kreuzer, A. Beispiele endlicher und unendlicher K-Loops. Results. Math. 23, 357–362 (1993). https://doi.org/10.1007/BF03322307
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DOI: https://doi.org/10.1007/BF03322307