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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Bibliographic Details
Published in:	Journal of algebra Vol. 181; no. 2; pp. 565 - 583
Main Authors:	Marciniak, Zbigniew S., Sehgal, Sudarshan K.
Format:	Journal Article
Language:	English
Published:	Elsevier Inc 15.04.1996
ISSN:	0021-8693, 1090-266X
Online Access:	Get full text
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Summary:	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.
ISSN:	0021-8693 1090-266X
DOI:	10.1006/jabr.1996.0134