×

Generalized theorem on the freedom for pro-p-groups. (Russian) Zbl 0599.20038

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

MSC:

20E18 Limits, profinite groups
20E10 Quasivarieties and varieties of groups
20F18 Nilpotent groups
20F05 Generators, relations, and presentations of groups
PDFBibTeX XMLCite
Full Text: EuDML