Free Groups in Subnormal Subgroups and the Residual Nilpotence of the Group of Units of Groups Rings
Canadian mathematical bulletin, Tome 27 (1984) no. 3, pp. 365-370
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Let KG be the group ring of the group G over the field K and U(KG) its unit group. When G is finite we derive conditions which imply that every noncentral subnormal subgroup of U(KG) contains a free group of rank two. We also show that residual nilpotence of U(KG) coincides with nilpotence, this being no longer true if G is infinite.We can answer partially the following question: when is G sub-normal in U(KG)?
Gonçalves, Jairo Z. Free Groups in Subnormal Subgroups and the Residual Nilpotence of the Group of Units of Groups Rings. Canadian mathematical bulletin, Tome 27 (1984) no. 3, pp. 365-370. doi: 10.4153/CMB-1984-055-6
@article{10_4153_CMB_1984_055_6,
author = {Gon\c{c}alves, Jairo Z.},
title = {Free {Groups} in {Subnormal} {Subgroups} and the {Residual} {Nilpotence} of the {Group} of {Units} of {Groups} {Rings}},
journal = {Canadian mathematical bulletin},
pages = {365--370},
year = {1984},
volume = {27},
number = {3},
doi = {10.4153/CMB-1984-055-6},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1984-055-6/}
}
TY - JOUR AU - Gonçalves, Jairo Z. TI - Free Groups in Subnormal Subgroups and the Residual Nilpotence of the Group of Units of Groups Rings JO - Canadian mathematical bulletin PY - 1984 SP - 365 EP - 370 VL - 27 IS - 3 UR - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1984-055-6/ DO - 10.4153/CMB-1984-055-6 ID - 10_4153_CMB_1984_055_6 ER -
%0 Journal Article %A Gonçalves, Jairo Z. %T Free Groups in Subnormal Subgroups and the Residual Nilpotence of the Group of Units of Groups Rings %J Canadian mathematical bulletin %D 1984 %P 365-370 %V 27 %N 3 %U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1984-055-6/ %R 10.4153/CMB-1984-055-6 %F 10_4153_CMB_1984_055_6
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