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. Oxford 47 (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. Oxford 47 (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. Oxford 47 (1996), 279-296].
Mattarei, S. (1999). Some thin pro-p-groups. JOURNAL OF ALGEBRA, 220(1), 56-72 [10.1006/jabr.1998.7809].
Some thin pro-p-groups
Mattarei, S
1999
Abstract
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. Oxford 47 (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. Oxford 47 (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. Oxford 47 (1996), 279-296].
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