Research on the impact of urbanization total factor carbon productivity is great significance to promote emission reductions and achieve sustainable development. Based panel data Central Asian countries from 1991 2019, SBM–Malmquist index model entropy method were used measure urbanization, respectively. The nonlinear regression, Tobit, quantile regression models empirically analyze in Asia. re...

in this article we introduce the notion of n-capable groups. it is shown that every group g admits a uniquely determined subgroup (〖z^n)〗^* (g) which is a characteristic subgroup and lies in the n-centre subgroup of the group g. this is the smallest subgroup of g whose factor group is n-capable. moreover, some properties of n-central extension will be studied.