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Soluble normally constrained pro-p-groups
-
Norberto Gavioli
,
Valerio Monti
Veröffentlicht/Copyright:
18. Juni 2007
Abstract
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.
Received: 2006-02-17
Revised: 2006-06-20
Published Online: 2007-06-18
Published in Print: 2007-05-23
© Walter de Gruyter
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- Transitivity properties for group actions on buildings
- Fields, values and character extensions in finite groups
- Primitive sharp permutation groups with large solvable subgroups
- On the size of the nilpotent residual in finite groups
- On the commuting complex of finite metanilpotent groups
- Soluble normally constrained pro-p-groups
- Comparing quasi-finitely axiomatizable and prime groups
- A finitely presented torsion-free simple group
- Andrews–Curtis groups and the Andrews–Curtis conjecture
- Residual finiteness of outer automorphism groups of certain tree products
- Commutator subgroups of Hantzsche–Wendt groups
Artikel in diesem Heft
- Transitivity properties for group actions on buildings
- Fields, values and character extensions in finite groups
- Primitive sharp permutation groups with large solvable subgroups
- On the size of the nilpotent residual in finite groups
- On the commuting complex of finite metanilpotent groups
- Soluble normally constrained pro-p-groups
- Comparing quasi-finitely axiomatizable and prime groups
- A finitely presented torsion-free simple group
- Andrews–Curtis groups and the Andrews–Curtis conjecture
- Residual finiteness of outer automorphism groups of certain tree products
- Commutator subgroups of Hantzsche–Wendt groups
