The ergodic actions of TICC groups preserving the finite measure and the II
1-factors constructed on these actions are studied in this paper. To distinguish between the II
1-factors, the properties of a centralizer of such actions are used. For SL(
n,
Z){\ominus}
Zn,
n≥3, a continuum of orbit (weakly) nonequivalent actions is constructed. Full II
1-factors having the properties opposite to the known properties of the hyperfinite factor are constructed. A full II
1-factor is presented, whose all tensor powers are non-isomorphic in pairs. It is shown that the full factor can coniain a non-isomorphic factor as a finite index subfactor and possess externally non-conjugated periodic automorphisms. Similar results are valid for ergodic equivalency relations.
The Supplement presents the principal points of the proof of the fact that the group SL(
n,
Z) for each
n≥3 has at least a countable number of orbit-nonequivalent actions preserving the finite measure.
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