Abstract:
Generalized left Bol 3-web $B_{l}(\rho,r,r)$ defined by action of an $r$-dimensional local smooth Bol quasigroup on $\rho$-dimensional manifold is considered. The following statement is proved: the Bol 3-web $B_{l}(\rho,r,r)$ can be realized as factor-web of a left Bol 3-web $B_{l}(r,r,r)$ which is formed by 3 $r$-dimensional foliations and its core coincides with the core of the given 3-web $B_{l}(\rho,r,r)$.
Keywords:Bol three-web, Bol quasigroup, factor-web, core of Bol 3-web.