Norberto Gavioli, Valerio Monti, Carlo Maria Scoppola
June 18, 2007
A pro- p -group G is said to be normally constrained (or, equivalently, of obliquity zero ) if every open normal subgroup of G is trapped between two consecutive terms of the lower central series of G . In this paper infinite soluble normally constrained pro- p- groups, for an odd prime p , are shown to be 2-generated. A classification of such groups, up to the isomorphism type of their associated Lie algebra, is provided in the finite coclass case, for p > 3. Moreover, we give an example of an infinite soluble normally constrained pro- p- group whose lattice of open normal subgroups is isomorphic to that of the Nottingham group. Some general results on the structure of soluble just infinite pro- p- groups are proved on the way.