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Keywords:
Bol loop action; Lie triple family; Nono family
Bol loop action; Lie triple family; Nono family
Summary:
The notions of left Bol and Bol-Bruck actions are introduced. A purely algebraic analogue of a Nono family (Lie triple family), the so called Sabinin-Nono family, is given. It is shown that any Sabinin-Nono family is a left Bol-Bruck action. Finally it is proved that any local Nono family is a local left Bol-Bruck action. On general matters see [L.V. Sabinin 91, 99].
References:
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Smooth Quasigroups and Loops. Kluwer Academic Publishers Dordrecht, The Netherlands (1999), xvi + 249 pp. MR 1727714 | Zbl 0939.20064
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