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Generators of Large Subgroups of Units of Integral Group Rings of Nilpotent Groups

✍ Scribed by A. Giambruno; S.K. Sehgal

Publisher: Elsevier Science
Year: 1995
Tongue: English
Weight: 207 KB
Volume: 174
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.1995.1121

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✦ Synopsis

Let (G) be a finite nilpotent group so that all simple components ((D){n \times n}, n \geq 2) of (Q G) satisfy the congruence subgroup theorem. Suppose that for all odd primes (p) dividing (|G|) the Hamiltonian quaternions (H) split over the (p) th cyclotomic field (Q\left(\zeta{p}\right)). Then new units (\mathscr{A}{3}) are introduced so that (\left\langle\mathscr{T}{1}, \mathscr{B}{2}, \mathscr{B}{2}^{\prime}, \mathscr{S}_{3}\right\rangle) is of finite index in (U(\mathbb{Z} G) . \bigcirc 1995) Academic Press, Inc.

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