Abstract
We argue against the conjecture which says that any two finite generating sets for G of the same cardinality are swap equivalent. The latter means that one is changed to another by a finite sequence of generating sets such that all the neighboring sets differ only in a single entry. Namely, it is proved that a free metabelian group of rank 3 has non swap equivalent bases.
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Additional information
Translated fromAlgebra i Logika, Vol. 34, No. 4, pp. 448–463, July-August, 1995.
Supported by the Russian Foundation for Fundamental Research.
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Roman'kov, V.A. The swap conjecture of tennant and turner. Algebr Logic 34, 249–257 (1995). https://doi.org/10.1007/BF00739409
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DOI: https://doi.org/10.1007/BF00739409