V. Ionin

Dimension subrings of Lie rings

We show that, unlike the lower central series, the dimension series of a Lie ring need not stabilize when two consecutive terms coincide; in fact, arbitrarily long finite plateaux occur. We prove that $D_n(L)/\gamma_{n+1}(L)$ is central in $L/\gamma_{n+1}(L)$ for every $n\geq1$, in contrast to the group case. If $c\geq...