Displaying similar documents to “Small profinite m-stable groups”

Constructing ω-stable structures: Computing rank

John T. Baldwin, Kitty Holland (2001)

Fundamenta Mathematicae

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This is a sequel to [1]. Here we give careful attention to the difficulties of calculating Morley and U-rank of the infinite rank ω-stable theories constructed by variants of Hrushovski's methods. Sample result: For every k < ω, there is an ω-stable expansion of any algebraically closed field which has Morley rank ω × k. We include a corrected proof of the lemma in [1] establishing that the generic model is ω-saturated in the rank 2 case.

Stable rank and real rank of compact transformation group C*-algebras

Robert J. Archbold, Eberhard Kaniuth (2006)

Studia Mathematica

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Let (G,X) be a transformation group, where X is a locally compact Hausdorff space and G is a compact group. We investigate the stable rank and the real rank of the transformation group C*-algebra C₀(X)⋊ G. Explicit formulae are given in the case where X and G are second countable and X is locally of finite G-orbit type. As a consequence, we calculate the ranks of the group C*-algebra C*(ℝⁿ ⋊ G), where G is a connected closed subgroup of SO(n) acting on ℝⁿ by rotation.

A note on groups of infinite rank whose proper subgroups are abelian-by-finite

Francesco de Giovanni, Federica Saccomanno (2014)

Colloquium Mathematicae

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It is proved that if G is a locally (soluble-by-finite) group of infinite rank in which every proper subgroup of infinite rank contains an abelian subgroup of finite index, then all proper subgroups of G are abelian-by-finite.

On the unit-1-stable rank of rings of analytic functions.

Joan Josep Carmona, Julià Cufí, Pere Menal (1992)

Publicacions Matemàtiques

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In this paper we prove a general result for the ring H(U) of the analytic functions on an open set U in the complex plane which implies that H(U) has not unit-1-stable rank and that has some other interesting consequences. We prove also that in H(U) there are no totally reducible elements different from the zero function.

Groups with all subgroups permutable or of finite rank

Martyn Dixon, Yalcin Karatas (2012)

Open Mathematics

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In this paper we investigate the structure of X-groups in which every subgroup is permutable or of finite rank. We show that every subgroup of such a group is permutable.