16.28 (2006)

Let $G$ be a connected linear reductive algebraic group over a field of positive characteristic, $X$ a closed subset of $G$, and let $X^k = \{x_1 \dots x_k \mid x_i \in X\}$.
$\qquad$ a) Is it true that there always exists a positive integer $c = c(X) > 1$ such that $X^c$ is closed?
$\qquad$ b) If $X$ is a conjugacy class of $G$ such that $X^2$ contains an open subset of $G$, then is $X^2 = G$?