1,720,973 research outputs found
Pro-p groups with waists
No full textA waist W of a pro-p group G is a subgroup which is comparable
with any open normal subgroup of G. The position of W with
respect to the terms of a central series of G is studied here. If p is
odd, with some natural hypotheses we show that W is a term of
both the lower and upper central series of G
Soluble Normally Constrained pro-p-groups
No full textA 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
Soluble normally constrained pro-p-groups
No full textA 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
Metabelian thin Lie algebras
No full textA graded Lie algebra is thin if it is generated by two elements of degree 1 and each of its homogeneous ideals is located between two consecutive terms of the lower central series. In this paper we give a complete classification of the metabelian thin Lie algebras and their graded automorphism groups
Profinite groups with finite virtual length
No full textIn this paper we introduce the notion of finite virtual length for profinite groups (that is, every series has a bounded number of infinite factors) and we prove a Jordan–Hölder type theorem for profinite groups with finite virtual length. More structural results are provided in the pronilpotent and p-adic analytic cases
Ideally constrained Lie Algebra
No full textAbstractIn this paper we deal with graded Lie algebras L such that there exists a positive integer r such that for every positive integer i and for every homogeneous ideal I⊈Li the inclusion I⊇Li+r−1 holds. The solvable case and the r=1 case receive a special attention
Soluble pro-p-groups and soluble Lie algebras
No full textWe present here some recent work on the correspondence between normal subgroups of profinite groups and graded ideals of their associated graded Lie algebras, and give characterizations of soluble just infinite pro-p-groups and modular soluble just infinite graded Lie algebras
Metabelian thin Lie algebras
No full textA graded Lie algebra is thin if it is generated by two elements of degree 1 and each of its homogeneous ideals is located between two consecutive terms of the lower central series. In this paper we give a complete classification of the metabelian thin Lie algebras and their graded automorphism groups. (C) 2001 Academic Press
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