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Finite Matrix Groups over Nilpotent Group Rings

✍ Scribed by Zbigniew S. Marciniak; Sudarshan K. Sehgal

Publisher: Elsevier Science
Year: 1996
Tongue: English
Weight: 216 KB
Volume: 181
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.1996.0134

No coin nor oath required. For personal study only.

✦ Synopsis

We study groups of matrices SGL ‫⌫ޚ‬ of augmentation one over the integral n Ž . group ring ‫⌫ޚ‬ of a nilpotent group ⌫. We relate the torsion of SGL ‫⌫ޚ‬ to the n Ž . torsion of ⌫. We prove that all abelian p-subgroups of SGL ‫⌫ޚ‬ can be stably n Ž . diagonalized. Also, all finite subgroups of SGL ‫⌫ޚ‬ can be embedded into the n n Ž . diagonal ⌫ -SGL ‫⌫ޚ‬ . We apply matrix results to show that if ⌫ is nilpotentn Ž X

. by-⌸ -finite then all finite ⌸-groups of normalized units in ‫⌫ޚ‬ can be embedded into ⌫.

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