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- Title
How to generalize known results on equations over groups.
- Authors
Klyachko, Anton A.
- Abstract
Known facts about the solvability of equations over groups are considered from a more general point of view. The theorem about the solvability of unimodular equations over torsion-free groups is generalized. A special case of the generalization is a multivariable version of this theorem. For unimodular equations over torsion-free groups, an analog of Magnus’ Freiheitssatz is proved, which asserts the existence of a solution exhibiting good behavior with respect to the free factors of the initial group.
- Subjects
FREE groups; GROUP theory; EQUATIONS; ALGEBRA; MULTIVARIATE analysis
- Publication
Mathematical Notes, 2006, Vol 79, Issue 3/4, p377
- ISSN
0001-4346
- Publication type
Article
- DOI
10.1007/s11006-006-0042-6