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\(\exists\)-free groups as groups with length function. (English. Russian original) Zbl 0784.20015
Ukr. Math. J. 44, No. 6, 733-738 (1992); translation from Ukr. Mat. Zh. 44, No. 6, 813-818 (1992).
It is proved that for any finitely generated group \(G\) there exists a length function (in the sense of R. C. Lyndon [Math. Scand. 12, 209-234 (1964; Zbl 0119.264)]) with values in a finitely generated group \(\Lambda\) for which \(G\) is a \(\Lambda\)-free group (in the sense of H. Bass [Arboreal Group theory 1988, Publ., Math. Sci. Res. Inst. 19, 69-131 (1991)]).

20F05 Generators, relations, and presentations of groups
20E05 Free nonabelian groups
20E08 Groups acting on trees
Full Text: DOI
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