Аннотация:
Let $D$ be a weakly locally finite division ring and $n$ a positive integer. In this paper, we investigate the problem on the existence of noncyclic free subgroups in noncentral almost subnormal subgroups of the general linear group $\mathrm{GL}_n(D)$. Further, some applications of this fact are also investigated. In particular, all infinite finitely generated almost subnormal subgroups of $\mathrm{GL}_n(D)$ are described.
Ключевые слова:division rings, linear groups, almost subnormal subgroups, noncyclic free subgroups, generalized group identity.