“School of Mathematics”
Back to Papers HomeBack to Papers of School of Mathematics
Paper IPM / M / 15380  


Abstract:  
Let R be a commutative ring of characteristic n ≥ 0 and G be a group. It is known that the group ring RG is bounded Lie Engel if and only if either G is nilpotent and G has a pabelian normal subgroup of finite ppower index (if n is a power of a prime p) or G is abelian. In this paper we try to generalize this result; if x and y are elements of RG, let [x,y]=xy−yx and inductively, [x, _{k} y]=[[x, _{k−1} y],y]. Let m and n be two natural numbers. Among other results, we show that if RG satisfies [x^{m}, _{n} y]=0, then either G′ is a pgroup (if n is a power of a prime p) or G is abelian. If G is locally finite, then we show that RG satisfies [x^{m(x,y)}, _{n(x,y)} y]=0 if and only if either G is locally nilpotent and G′ is a pgroup (if n is a power of a prime p) or G is abelian.
Download TeX format 

back to top 