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Generation of finite groups by nilpotent subgroups

E. Damian (2003)

Bollettino dell'Unione Matematica Italiana

We study the generation of finite groups by nilpotent subgroups and in particular we investigate the structure of groups which cannot be generated by n nilpotent subgroups and such that every proper quotient can be generated by n nilpotent subgroups. We obtain some results about the structure of these groups and a lower bound for their orders.

Geometric subgroups of surface braid groups

Luis Paris, Dale Rolfsen (1999)

Annales de l'institut Fourier

Let M be a surface, let N be a subsurface, and let n m be two positive integers. The inclusion of N in M gives rise to a homomorphism from the braid group B n N with n strings on N to the braid group B m M with m strings on M . We first determine necessary and sufficient conditions that this homomorphism is injective, and we characterize the commensurator, the normalizer and the centralizer of π 1 N in π 1 M . Then we calculate the commensurator, the normalizer and the centralizer of B n N in B m M for large surface braid...

Gradients de Heegaard sous-logarithmiques d’une variété hyperbolique de dimension trois et fibres virtuelles

Claire Renard (2010/2011)

Séminaire de théorie spectrale et géométrie

J. Maher a montré qu’une variété hyperbolique de dimension 3 compacte sans bord, connexe et orientable fibre virtuellement sur le cercle si et seulement si elle admet une famille infinie de revêtements finis de genre de Heegaard borné. En s’appuyant sur la démonstration de Maher, cet article présente un théorème donnant une condition suffisante pour qu’un revêtement fini d’une variété hyperbolique compacte de dimension 3 contienne une fibre virtuelle, qui s’exprime en fonction du degré d du revêtement...

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