Nilpotent elements in group rings

descriptionPublicationkeyboard_double_arrow_right Article 01 Mar 1975 Germany English Publisher:Springer Science and Business Media LLCJournal:Manuscripta Mathematica, volume 15, pages 65-80 (issn: 0025-2611, eissn: 1432-1785,

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Authors: Sehgal, Sudarshan K.;

doi: 10.1007/bf01168879

Nilpotent elements in group rings

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Abstract

The main theorem gives necessary and sufficient conditions for the rational group algebra QG to be without (nonzero) nilpotent elements if G is a nilpotent or F·C group. For finite groups G, a characterisation of group rings RG over a commutative ring with the same property is given. As an application those nilpotent or F·C groups are characterised which have the group of units U(KG) solvable for certain fields K.

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Germany

Related Organizations

University of Alberta
Canada
DigiZeitschriften
Germany

Keywords

510.mathematics, General structure theorems for groups, Group rings, Chains and lattices of subgroups, subnormal subgroups, Article, Local properties of groups

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