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A group of operators G in a space without G-torsion. (English. Russian original) Zbl 0576.06019
Sib. Math. J. 25, 845-849 (1984); translation from Sib. Mat. Zh. 25, No. 6(148), 17-22 (1984).
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.
Reviewer: C.G.Chehata
MSC:
 06F20 Ordered abelian groups, Riesz groups, ordered linear spaces 47D03 Groups and semigroups of linear operators 20C99 Representation theory of groups
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References:
 [1] V. V. Bludov, ?Example of an unorderable group with strictly isolated identity,? Algebra Logika, No. 11, 619-632 (1972). [2] R. B. Mura and A. H. Rhemtulla, ?Solvable R*-groups,? Math. Z.,142, No. 3, 293-298 (1975). · Zbl 0295.20036 · doi:10.1007/BF01183052
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