This article is cited in 12 papers

How to generalize known results on equations over groups

A. A. Klyachko

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

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.

UDC: 512.543.7

Received: 22.12.2003
Revised: 29.08.2005

DOI: 10.4213/mzm2710

 English version: Mathematical Notes, 2006, 79:3, 377–386

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