Abstract
Bol [66] was the first to construct a commutative Moufang loop which is not an abelian group. Each of Bol’s examples is centrally nil-potent of class 2. Bruck [70] showed how to construct examples which are centrally nilpotent of class 3. In his University of Wisconsin thesis (1953), T. Slaby formulated the following theorem: Every commutative Moufang loop which can be generated by n elements (n > 1) is centrally nilpotent of class at most n — 1. In collaboration with the author, Slaby proved this theorem for n = 4, 5 as well as for the previously known cases n = 2, 3.
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© 1971 Springer-Verlag Berlin Heidelberg
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Bruck, R.H. (1971). Commutative Moufang Loops. In: A Survey of Binary Systems. Ergebnisse der Mathematik und ihrer Grenzgebiete, vol NF 20. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-43119-1_8
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DOI: https://doi.org/10.1007/978-3-662-43119-1_8
Publisher Name: Springer, Berlin, Heidelberg
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