How to generalize known results on equations over groups
群论
2007-05-23 v4
摘要
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.
引用
@article{arxiv.math/0406382,
title = {How to generalize known results on equations over groups},
author = {Anton A. Klyachko},
journal= {arXiv preprint arXiv:math/0406382},
year = {2007}
}
备注
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.msu.su/department/algebra/staff/klyachko/papers.htm