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math.GR2004★ 19 cited
The number of non-solutions to an equation in a group and non-topologizable torsion-free groups
Anton A. Klyachko, Anton V. Trofimov
It is shown that, for any pair of cardinals with infinite sum, there exist a group and an equation over this group such that the first cardinal is the number of solutions to this e…
math.GR2004★ 16 cited
How to generalize known results on equations over groups
Anton A. Klyachko
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 eq…