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Article

Keywords:
Bol loop; K-loop; Bruck loop
Summary:
If the left multiplication group of a loop is simple, then the loop is simple. We use this observation to give examples of infinite simple Bol loops.
References:
[1] Aschbacher M., Kinyon M.K., Phillips J.D.: Finite Bruck loops. submitted. Available at http://www.arXiv.org/abs/math.GR/0401193 Zbl 1102.20046
[2] Bruck R.H.: A Survey of Binary Systems. Springer-Verlag, Berlin-Heidelberg-New York, 1971; MR 20{#}76, Zbl. 206:30301. MR 0093552 | Zbl 0141.01401
[3] Foguel T., Ungar A.A.: Gyrogroups and the decomposition of groups into twisted subgroups and subgroups. Pacific J. Math. 197 (2001), 1-11; MR 2002e:20142, Zbl. pre01589578. MR 1810204 | Zbl 1066.20068
[4] Huppert B.: Endliche Gruppen I. Springer-Verlag, Berlin-Heidelberg-New York, 1967; MR 37 {#}302, Zbl. 0217.07201. MR 0224703 | Zbl 0412.20002
[5] Kiechle H.: Theory of K-loops. Lecture Notes in Math. 1778, Springer-Verlag, Berlin-Heidelberg-New York, 2002; MR 2003d:20109, Zbl. 0997.20059. MR 1899153 | Zbl 0997.20059
[6] Nagy P.T., Strambach K.: Loops in Group Theory and Lie Theory. de Gruyter Expositions in Mathematics 35, Walter de Gruyter, Berlin-New York, 2003; MR 2003d:20110, Zbl. pre01732502. MR 1899331 | Zbl 1050.22001
[7] Rózga K.: On central extensions of gyrocommutative gyrogroups. Pacific J. Math. 193 (2000), 201-218; MR 2001a:20115, Zbl. 1010.20055. MR 1748188
[8] Scott W.R.: Group Theory. Dover, New York, 1987; MR 88d:20001, Zbl. 0641.20001. MR 0896269 | Zbl 0897.20029
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