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We consider the geometric and algebraic properties of a locally symmetric differentiable manifold of an affine connection. The identities in the geodesic loop of a symmetric affine connection space are discussed. Using the left Bol identity, which the geodesic loop satisfies at © Андроникова Е.О., Матвеев О.А., 2017. ISSN 2072-8387 Вестник Московского государственного областного университета. Серия: Физика-Математика 2017 / No 3 7 each point of space, we derive an algebraic identity that is satisfied by the geodesic symmetries of locally flat spaces. The results obtained are used to solve construction problems.

THE LEFT BOL IDENTITY IN THE THEORY OF SYMMETRIC SPACES WITH AN AFFINE CONNECTION