2 problems

Regular-language conjecture. $H$ is stable if and only if $L_H^{(k,c)}$ is regular whenever $k$ is rational.

Let $A(\Gamma)$ be a right-angled Artin group whose defining graph $\Gamma$ is connected and not a join, and let $H$ be a stable subgroup of $A(\Gamma)$. Let $(\mu_i)$ be a sequenc…