How to generalize known results on equations over groups

Details How to generalize known results on equations over groups How to generalize known results on equations over groups

2004-06-18

arxiv.org/abs/math/0406382v4

Mathematical Notes, 2006, 79:3, 377-386. Translated from Matematicheskie Zametki, 2006, 79:3, 409-419

Mathematics

Group Theory

9 pages. V.4: minor corrections in the proof of the main theorem (p.5). Russian version of this paper is at http://mech.math

Scientific paper

10.1007/s11006-006-0042-6

The known facts about solvability of equations over groups are considered from a more general point of view. A generalized version of the theorem about solvability of unimodular equations over torsion-free groups is proved. In a special case, this generalized version become a multivariable variant of this theorem. For unimodular equations over torsion free groups, we prove an analogue of Magnus's Freiheitssatz, which asserts that there exists a solution with good behavior with respect to free factors of the initial group.

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