Some thin pro-p-groups

A pro-p-group is called thin if its lattice of closed normal subgroups contains no more than p + 1 pairwise incomparable elements. An investigation of certain (infinite) thin pro-p-groups was made in [A. Caranti et al. Quart. J. Math. Oxford47 (1996), 279–296], by studying the graded Lie algebras associated with their lower central series. In particular, the main result of [A. Caranti et al. Quart. J. Math. Oxford47 (1996), 279–296] asserts that those graded Lie algebras are, in certain cases, uniquely determined by their quotients of low dimension. In the present paper we construct pro-p-groups which have, associated with their lower central series, the graded Lie algebras of [A. Caranti et al. Quart. J. Math. Oxford47 (1996), 279–296]