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This article is cited in 18 scientific papers (total in 18 papers)
A freedom theorem for groups with one defining relation in the varieties of solvable and nilpotent groups of given lengths
N. S. Romanovskii
Abstract:
The freedom theorem of Magnus is well known: if a group $G$ is given by generators $x_1,x_2,\dots$ and a single defining relation $r=1$, and if $r$ is not conjugate to any word in $x_2,\dots$, then the elements $x_2,\dots$ freely generate in $G$ a free subgroup. In this note analogous theorems of Magnus are established for groups given by one defining relation in the varieties of soluble and nilpotent groups of given lengths.
Bibliography: 7 titles.
Received: 12.07.1971
Citation:
N. S. Romanovskii, “A freedom theorem for groups with one defining relation in the varieties of solvable and nilpotent groups of given lengths”, Math. USSR-Sb., 18:1 (1972), 93–99
Linking options:
https://www.mathnet.ru/eng/sm3219https://doi.org/10.1070/SM1972v018n01ABEH001614 https://www.mathnet.ru/eng/sm/v131/i1/p93
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