How to Generalize the Known Results on Equations over Group
نویسنده
چکیده
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 (ordinary and generalized) 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.
منابع مشابه
How to Generalize the Known Results on Equations over Groups
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...
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