Romanovskij, N. S. Generalized theorem on the freedom for pro-p-groups. (Russian) Zbl 0599.20038 Sib. Mat. Zh. 27, No. 2(156), 154-170 (1986). The generalized theorem on the freedom for a quasi-variety M declares that if an algebra from M is generated by an n-element set X under m relations, \(m<n\), then X contains an (n-m)-element subset freely generating a free M-algebra. The author proves the theorem for the class of all pro-p-groups, for each variety of k-step solvable pro-p-groups or k-step nilpotent pro-p-groups. As a corollary the theorem is proved for the variety of all k-step nilpotent groups. Reviewer: Yu.Mukhin Cited in 3 ReviewsCited in 4 Documents MSC: 20E18 Limits, profinite groups 20E10 Quasivarieties and varieties of groups 20F18 Nilpotent groups 20F05 Generators, relations, and presentations of groups Keywords:quasi-variety; relations; free M-algebra; solvable pro-p-groups; nilpotent pro-p-groups PDFBibTeX XMLCite \textit{N. S. Romanovskij}, Sib. Mat. Zh. 27, No. 2(156), 154--170 (1986; Zbl 0599.20038) Full Text: EuDML