Speciality:
01.01.06 (Mathematical logic, algebra, and number theory)
Birth date:
05.06.1947
E-mail: Keywords: ordered groups; groups of automorphisms of ordered sets.
Subject:
A theory of orderable representations of groups was developed both be applied in the study of the structure of right-orderable groups, and representing a value of its own. Lattices of right-relative convex subgroups of right-orderable groups were studied. Factor groups of right-orderable groups were found to be right-orderable for some divisible normal, namely divisible central subgroups. A description of right-orderable groups permitting a finite number of right orders, and groups with a finite number of right-relative convex subgroups was obtained. It is shown that radical right-orderable groups are locally indicable. An example of a right-orderable group that is not locally indicable was constructed. We show that an 0-2-transitive group of order automorphisms of a linearly ordered set with Abelian stabilizer of a point is a subgroup of the affine permutation group of a linearly ordered field. The theory of cl-groups of automorphisms of cyclically ordered sets that play the same role in the theory of groups of automorphisms of cyclically ordered sets as lattice-ordered groups of automorphisms do in the theory of groups of automorphisms of linearly ordered sets was constructed. A classification of transitive c-primitive cl-groups of automorphisms of cyclically ordered sets was produced.
Main publications:
Tararin V. M. K teorii pravouporyadochivaemykh grupp // Matem. zametki, 1993, 54(2), 96–98.
Tararin V. M. O vypuklykh podgruppakh pravouporyadochennykh grupp // Sib. matem. zhurn., 1994, 35(5), 1165–1170.
Tararin V. M. 0-2-Tranzitivnye gruppy avtomorfizmov s abelevym stabilizatorom tochki // Matem. zametki, 1999, 65(2), 289–293.
Tararin V. M. O gruppakh avtomorfizmov tsiklicheski uporyadochennykh mnozhestv // Sib. matem. zhurn., 2001, 42(1), 212–230.
