Resumen de Sobre radicales finitos y linealidad residual de grupos nilpotentes

Pere Menal Brufal

• SET K(G) BE SHE GRONP RING OF G OVER SHE FIELD K, THE FINITE RADICAL OF K(G) (F*-R(K(G) IS THE INTERSECTION OF SHE RERNELS OF AEL ITS FINITE REPRESENTATIONS. FIRST WE GIVE ELEMENTARY RESUELT FOR THE FINITE RADICAL OF K(G) IS EQUIVALENT TO RESIDUAL LINEARITY. WE STUDY SHIS QUESTION FOR NIEPOTENT GROUPS. FOR NINITELY GENERALITED GROUPS IT IS WELL RNOWN (MAL'EN) HRAT RESIDUAYLLY LINEAR AND RESIDUALLY FINITE ARE EQUIVALENT. WE OFFER A GENERALIZATION AND CONSTEREXAMPLES. FINALLY LET R BE A RING. WE FIND NECESSARY AND SUFFICENT CONDITIONS FOR R IN ORDER SHAT THE GRUOPS GL(M.R) TR(M R) TN( R) FOR N 3 TO BE RESIDUALLY FINITE. IF N=2 WE GIVE RAME PARTIAL CONVERSE.