How can I look to the semidirect product $G_n$ of $A_n = \Bbb{F}_p[X]/(X^{p^n} - 1)$ by $\langle x_n \rangle \simeq \Bbb{Z}/p^n\Bbb{Z}$ with $x_n$ acting as multiplication by $X$? I want to calculate the number of topological generators of $\varprojlim G_n$ w.r.t natural projections $A_{n+1} \t...