Non-trivial GPCGI conjecture for almost subnormal subgroups of general linear groups

Let $D$ be a division ring with center $F$, and let $\operatorname{GL}_n(D)$ be the general linear group of degree $n$ over $D$. If $n\geq 2$, assume that $D$ is not a locally finite field. Let

$$w(x_1,x_2,\dots,x_m)=a_1x_{i_1}^{\alpha_1}a_2x_{i_2}^{\alpha_2}\cdots a_tx_{i_t}^{\alpha_t}a_{t+1}$$

be a generalized group monomial over $\operatorname{GL}_n(D)$. If $N$ is an almost subnormal subgroup of $\operatorname{GL}_n(D)$ and $w$ is a non-trivial generalized power central group identity of $N$, then $N$ is central. The almost-subnormal GPCGI conjecture. Under these hypotheses, $N$ is central. The conjecture extends the question of whether non-trivial generalized power central group identities can occur in non-central almost subnormal subgroups; the supplied text gives no resolution status.