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Products of Free Groups in the Unit Group of Integral Group Rings

✍ Scribed by Eric Jespers; Guilherme Leal; Angel del Rı́o

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
253 KB
Volume
180
Category
Article
ISSN
0021-8693

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✦ Synopsis

We classify the nilpotent finite groups G which are such that the unit group Ž . U U ZG of the integral group ring ZG has a subgroup of finite index which is the direct product of noncyclic free groups. It is also shown that nilpotent finite groups having this property can be characterised by means of the Wedderburn decomposition of the rational group algebra QG.

📜 SIMILAR VOLUMES

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We classify all the finite groups G, such that the group of units of ZG contains a subgroup of finite index which is isomorphic to a direct product of nonabelian free Ž groups. This completes the work of Jespers, Leal, and del Rıo J. Algebra 180 Ž . . 1996 , 22᎐40 , where the nilpotent groups with

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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}\

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✍ E. Jespers; S.O. Juriaans 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 138 KB

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