Abstract: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. \par 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].
Keywords: Bol loop action, Lie triple family, Nono family
AMS Subject Classification: 20N05