A~freedom theorem for groups with one defining relation in the varieties of solvable and nilpotent groups of given lengths
Sbornik. Mathematics, Tome 18 (1972) no. 1, pp. 93-99
Voir la notice de l'article provenant de la source Math-Net.Ru
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.
@article{SM_1972_18_1_a5,
author = {N. S. Romanovskii},
title = {A~freedom theorem for groups with one defining relation in the varieties of solvable and nilpotent groups of given lengths},
journal = {Sbornik. Mathematics},
pages = {93--99},
publisher = {mathdoc},
volume = {18},
number = {1},
year = {1972},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_1972_18_1_a5/}
}
TY - JOUR AU - N. S. Romanovskii TI - A~freedom theorem for groups with one defining relation in the varieties of solvable and nilpotent groups of given lengths JO - Sbornik. Mathematics PY - 1972 SP - 93 EP - 99 VL - 18 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/SM_1972_18_1_a5/ LA - en ID - SM_1972_18_1_a5 ER -
%0 Journal Article %A N. S. Romanovskii %T A~freedom theorem for groups with one defining relation in the varieties of solvable and nilpotent groups of given lengths %J Sbornik. Mathematics %D 1972 %P 93-99 %V 18 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/item/SM_1972_18_1_a5/ %G en %F SM_1972_18_1_a5
N. S. Romanovskii. A~freedom theorem for groups with one defining relation in the varieties of solvable and nilpotent groups of given lengths. Sbornik. Mathematics, Tome 18 (1972) no. 1, pp. 93-99. http://geodesic.mathdoc.fr/item/SM_1972_18_1_a5/