Finite Matrix Groups over Nilpotent Group Rings Original Research Article

We study groups of matricesSGLn(imageΓ) of augmentation one over the integral group ring imageΓ of a nilpotent group Γ. We relate the torsion ofSGLn(imageΓ) to the torsion of Γ. We prove that all abelianp-subgroups ofSGLn(imageΓ) can be stably diagonalized. Also, all finite subgroups ofSGLn(imageΓ) can be embedded into the diagonal Γn