Linear representations of soluble groups of finite Morley rank
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- by Tuna Altınel and John S. Wilson PDF
- Proc. Amer. Math. Soc. 139 (2011), 2957-2972 Request permission
Abstract:
Sufficient conditions are given for groups of finite Morley rank having nontrivial torsion-free nilpotent normal subgroups to have linear representations with small kernels. In particular, centreless connected soluble groups of finite Morley rank with torsion-free Fitting subgroups have faithful linear representations. Along the way, using a notion of definable weight space, we prove that certain connected soluble groups of finite Morley rank with torsion-free derived subgroup can be embedded in groups of finite Morley rank whose Fitting subgroups have definable abelian supplements.References
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Additional Information
- Tuna Altınel
- Affiliation: Institut Camille Jordan, Université Lyon 1, 43 boulevard du 11 novembre 1918, 69622 Villeurbanne cedex, France
- Email: altinel@math.univ-lyon1.fr
- John S. Wilson
- Affiliation: University College, Oxford OX1 4BH, United Kingdom
- Email: wilsonjs@maths.ox.ac.uk
- Received by editor(s): September 26, 2009
- Received by editor(s) in revised form: July 20, 2010
- Published electronically: December 29, 2010
- Additional Notes: The first author was partially supported by the ANR project “Groupes, Géométrie et Logique” JC05 47037:jaligot:eric.
Both authors acknowledge the support of FAW - Communicated by: Julia Knight
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 139 (2011), 2957-2972
- MSC (2010): Primary 03C60, 20F16
- DOI: https://doi.org/10.1090/S0002-9939-2010-10713-X
- MathSciNet review: 2801636