Lower central series and derived series of net subgroups of the general linear group

Over a commutative ring $R$ with invertible element 2 and with radical $\mathfrak J$, nets (i.e., tables $\sigma=(\sigma_{ij})$ of ideals $\sigma_{ij}$ such that $\sigma_{i\Gamma}\sigma_{\Gamma j}\subset\sigma_{ij}$) such that $\sigma_{ii}\subset\mathfrak J$ are considered. Such nets are called pseudoradical. The groups of the lower central series and the derived series are explicitly constructed for the corresponding net subgroups $G(\sigma)$ (of the general linear group $GL(n,R)$) in terms of $\sigma$.