Varieties of pro-\(p\)-groups of second order matrices (Q1814499)

The author proves that an arbitrary proper subvariety of the variety of pro-\(p\)-groups \(V_ 0\) generated by the pro-\(p\)-group of generic matrices of order 2 is contained either in \(N_ cA\) or in \(V_ mN_ cA\), where \(m\) and \(c\geq 1\), \(p\neq 2\). Here \(V_ m\) is the variety of pro-\(p\)-groups generated by the pro-\(p\)-group of generic matrices of order 2 over \(\mathbb{Z}/p^ m\mathbb{Z}\), \(N_ c\) is the variety of all nilpotent pro-\(p\)-groups of class not greater than \(c\), \(A\) is the variety of the all Abelian pro-\(p\)-groups.