On some \(\Lambda\)-analytic pro-\(p\) groups (Q1320037)

Let \(\Lambda\) be a complete commutative Noetherian local ring whose residual field is finite. A notion of \(\Lambda\)-standard group over \(\Lambda\) is defined and a Lie algebra \(L_ 0\) is associated with it. \(G\) is called \(\Lambda\)-perfect if \(L_ 0 = L_ 0'\), and two growth functions for \(G\) are studied, an analog of the Golod-Shafarevich inequality is proved. Two problems of N. Boston are settled.