On the Cantor-Bendixson rank of metabelian groups

Yves Cornulier

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Displaying similar documents to “On the Cantor-Bendixson rank of metabelian groups”

Linear maps preserving orbits

Gerald W. Schwarz (2012)

Annales de l’institut Fourier

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Let $H \subset GL (V)$ be a connected complex reductive group where $V$ is a finite-dimensional complex vector space. Let $v \in V$ and let $G = {g \in GL (V) ∣ g H v = H v}$ . Following Raïs we say that the orbit $H v$ is if the identity component of $G$ is $H$ . If $H$ is semisimple, we say that $H v$ is for $H$ if the identity component of $G$ is an extension of $H$ by a torus. We classify the $H$ -orbits which are not (semi)-characteristic in many cases.

Relative property (T) and linear groups

Talia Fernós (2006)

Annales de l’institut Fourier

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Relative property (T) has recently been used to show the existence of a variety of new rigidity phenomena, for example in von Neumann algebras and the study of orbit-equivalence relations. However, until recently there were few examples of group pairs with relative property (T) available through the literature. This motivated the following result: A finitely generated group $Γ$ admits a special linear representation with non-amenable $R$ -Zariski closure if and only if it acts on an Abelian...

A minimal Set of Generators for the Ring of multisymmetric Functions

David Rydh (2007)

Annales de l’institut Fourier

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The purpose of this article is to give, for any (commutative) ring $A$ , an explicit minimal set of generators for the ring of multisymmetric functions ${T S}_{A}^{d} (A [x_{1}, \dots, x_{r}]) = {(A {[x_{1}, \dots, x_{r}]}^{\otimes_{A} d})}^{𝔖_{d}}$ as an $A$ -algebra. In characteristic zero, i.e. when $A$ is a $ℚ$ -algebra, a minimal set of generators has been known since the 19^th century. A rather small generating set in the general case has also recently been given by Vaccarino but it is not minimal in general. We also give a sharp degree bound on the generators, improving...

On some elementary properties of soluble groups of derived length 2.

Romanovskij, N. S., Timoshenko, E. I. (2003)

Sibirskij Matematicheskij Zhurnal

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Ramification and moduli spaces of finite flat models

Naoki Imai (2011)

Annales de l’institut Fourier

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We determine the type of the zeta functions and the range of the dimensions of the moduli spaces of finite flat models of two-dimensional local Galois representations over finite fields. This gives a generalization of Raynaud’s theorem on the uniqueness of finite flat models in low ramifications.

Systolic invariants of groups and $2$ -complexes via Grushko decomposition

Yuli B. Rudyak, Stéphane Sabourau (2008)

Annales de l’institut Fourier

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We prove a finiteness result for the systolic area of groups. Namely, we show that there are only finitely many possible unfree factors of fundamental groups of $2$ -complexes whose systolic area is uniformly bounded. We also show that the number of freely indecomposable such groups grows at least exponentially with the bound on the systolic area. Furthermore, we prove a uniform systolic inequality for all $2$ -complexes with unfree fundamental group that improves the previously known bounds...

Displaying similar documents to “On the Cantor-Bendixson rank of metabelian groups”

Linear maps preserving orbits

Relative property (T) and linear groups

A minimal Set of Generators for the Ring of multisymmetric Functions

On some elementary properties of soluble groups of derived length 2.

Ramification and moduli spaces of finite flat models

Systolic invariants of groups and 2 -complexes via Grushko decomposition

Systolic invariants of groups and $2$ -complexes via Grushko decomposition