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The smallest Moufang loop revisited. (English) Zbl 1050.20046

O. Chein and H. O. Pflugfelder proved that the smallest nonassociative Moufang loop is of order 12 and is unique up to isomorphism. In this paper a new, visual description of this loop is given.

MSC:

20N05 Loops, quasigroups
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References:

[1] O. Chein, Moufang Loops of Small Order I, Trans. Amer. Math. Soc. 188 (1974), 31–51. · Zbl 0286.20088 · doi:10.1090/S0002-9947-1974-0330336-3
[2] O. Chein, Moufang Loops of Small Order, Memoirs of the American Mathematical Society, Volume 13, Issue 1, Number 197 (1978). · Zbl 0378.20053
[3] O. Chein, H. O. Pflugfelder, The smallest Moufang loop, Arch. Math. 22 (1971), 573–576. · Zbl 0241.20061 · doi:10.1007/BF01222620
[4] K. Kunen, Moufang Quasigroups, J. Algebra 183 (1996), no 1, 231–234. · Zbl 0855.20056 · doi:10.1006/jabr.1996.0216
[5] H. O. Pflugfelder, Quasigroups and Loops: Introduction, (Sigma series in pure mathematics; 7), Heldermann Verlag Berlin (1990). · Zbl 0715.20043
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