𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Measurable groups of low dimension

✍ Scribed by Richard Elwes; Mark Ryten

Publisher
John Wiley and Sons
Year
2008
Tongue
English
Weight
176 KB
Volume
54
Category
Article
ISSN
0044-3050

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

We consider low‐dimensional groups and group‐actions that are definable in a supersimple theory of finite rank. We show that any rank 1 unimodular group is (finite‐by‐Abelian)‐by‐finite, and that any 2‐dimensional asymptotic group is soluble‐by‐finite. We obtain a field‐interpretation theorem for certain measurable groups, and give an analysis of minimal normal subgroups and socles in groups definable in a supersimple theory of finite rank where infinity is definable. We prove a primitivity theorem for measurable group actions. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

📜 SIMILAR VOLUMES

Isometry Dimension of Finite Groups
Isometry Dimension of Finite Groups
✍ Manish M. Patnaik 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 94 KB

We show that the isometry dimension of a finite group G is equal to the dimension of a minimal-dimensional faithful real representation of G. Using this result, we answer several questions of Albertson and Boutin [J. Algebra 225 (2000), 947-955 .

Comparison of Picard groups in dimension
Comparison of Picard groups in dimension 1
✍ Henri Lombardi; Claude Quitté 📂 Article 📅 2008 🏛 John Wiley and Sons 🌐 English ⚖ 102 KB

## Abstract We compare two Picard groups in dimension 1. Our proofs are constructive and the results generalize a theorem of J. Sands [11]. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Affine Distance-transitive Groups of Dim
Affine Distance-transitive Groups of Dimension One
✍ Arjeh M. Cohen; Alexander A. Ivanov 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 77 KB

containing the translations and acting primitively on the set of vectors in V . Let G 0 be the stabilizer in G of the zero vector, so that G 0 ≤ L(V ) ∼ = L(1, q) and G = V : G 0 . Suppose that is a graph structure on V on which G acts distance-transitively. Such graphs of diameter at most 2 are kno

Transitive Actions of Compact Groups and
Transitive Actions of Compact Groups and Topological Dimension
✍ Karl H. Hofmann; Sidney A. Morris 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 199 KB

## dedicated to helmut wielandt on the occasion of his 90th birthday There are many dimension functions defined on arbitrary topological spaces taking either a finite value or the value infinity. This paper defines a cardinal valued dimension function, dim. The Lie algebra G of a compact group G i

On Rigid Tuples in Linear Groups of Odd
On Rigid Tuples in Linear Groups of Odd Dimension
✍ Michael Dettweiler; Stefan Reiter 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 99 KB

We construct examples of linearly rigid tuples which lead to regular Galois Ž . Ž 2 . realizations over ‫ޑ‬ for linear and unitary groups GL q and U q , where q is odd and m ) q y 1 resp. m ) q q 1 . The notion of linear Ž rigidity was introduced by Strambach and Volklein J. Reine Angew. Math., to