Alternative real linear spaces of dimensions 2, 3 and 4

The article considers Abelian subgroups of real unitriangular groups of the third, fourth and fifth orders and isomorphic to them - tuple length groups of 2, 3, 4 real numbers. The authors receive linear spaces alternative to arithmetical space on the basis of tuple length groups. Operations over alternative space vectors are set by nonlinear formulas. Groups of automorphism spaces of one dimension are set by nonlinear formulas of a various kind. All considered linear spaces are subsibsons. The article defines sibsons of dimensions 3, 6, 10.