11.105 (1990)

Its relatively free group of given rank has a presentation $F/N$, where $F$ is absolutely free of the same rank and $N$ fully invariant in $F$. The associated Lie ring $\mathscr{L}(F/N)$ has a presentation $L/J$, where $L$ is the free Lie ring of the same rank and $J$ an ideal of $L$.
$\qquad$ a) Is $J$ always fully invariant in $L$ if $\mathfrak{V}$ is any variety of groups?
$\qquad$ b) Is $J$ fully invariant in $L$ if $\mathfrak{V}$ is the Burnside variety of all groups of given exponent $q$, where $q$ is a prime-power, $q \geqslant 4$?