For any connected Lie group G, we introduce the notion of exponential radical Exp G that is the set of all strictly exponentially distorted elements of G. In case G is a connected simply-connected solvable Lie group, we prove that Exp G is a connected normal Lie subgroup in G and the exponential rad
Linearly Equivalent Actions of Solvable Groups
β Scribed by B. de Smit; H.W. Lenstra Jr.
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 134 KB
- Volume
- 228
- Category
- Article
- ISSN
- 0021-8693
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β¦ Synopsis
We determine the positive integers n for which there exist a solvable group G and two non-conjugate subgroups of index n in G that induce the same permutation character.
π SIMILAR VOLUMES
S n show that the fixed field K x , . . . , x is rational over K. Similar results for 1 n actions of S on the symmetric powers and exterior powers of V [ [ n K ΠΈ x are n i is1 valid.
Let β«ήβ¬ be a connected, solvable linear algebraic group over a number field K, let Ε½ . S be a finite set of places of K that contains all the infinite places, and let O O S be the ring of S-integers of K. We define a certain closed subgroup β«ήβ¬ of β«ήβ¬ s Ε β«ήβ¬ that contains β«ήβ¬ , and prove that β«ήβ¬