Finite Matrix Groups over Nilpotent Group Rings
We study groups of matricesSGLn(ZΓ) of augmentation one over the integral group ring ZΓ of a nilpotent group Γ. We relate the torsion ofSGLn(ZΓ) to the torsion of Γ. We prove that all abelianp-subgroups ofSGLn(ZΓ) can be stably diagonalized. Also, all finite subgroups ofSGLn(ZΓ) can be embedded into...
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| Veröffentlicht in: | Journal of algebra Jg. 181; H. 2; S. 565 - 583 |
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| Hauptverfasser: | , |
| Format: | Journal Article |
| Sprache: | Englisch |
| Veröffentlicht: |
Elsevier Inc
15.04.1996
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| ISSN: | 0021-8693, 1090-266X |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | We study groups of matricesSGLn(ZΓ) of augmentation one over the integral group ring ZΓ of a nilpotent group Γ. We relate the torsion ofSGLn(ZΓ) to the torsion of Γ. We prove that all abelianp-subgroups ofSGLn(ZΓ) can be stably diagonalized. Also, all finite subgroups ofSGLn(ZΓ) can be embedded into the diagonal Γn<SGLn(ZΓ). We apply matrix results to show that if Γ is nilpotent-by-(Π′-finite) then all finite Π-groups of normalized units in ZΓ can be embedded into Γ. |
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| ISSN: | 0021-8693 1090-266X |
| DOI: | 10.1006/jabr.1996.0134 |