A group of operators G in a space without G-torsion (Q1065045)

It is known that if in a linear space \(L_ n(K)\) with group G of operators there exists a G-invariant linear order, then it has no G- torsion. But also examples of a space without G-torsion in which there is no G-invariant order are known. The author obtains in this paper necessary and sufficient conditions for (1) each of the spaces \(L_ n(R)\), \(L_ n(Q)\) with group G of operators to have no G-torsion, and (2) \(L_ n(Q)\) to have a G-invariant linear order.