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

✍ Scribed by Guilherme Leal; Angel del Rı́o

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
221 KB
Volume
191
Category
Article
ISSN
0021-8693

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✦ Synopsis

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 this property are given.

📜 SIMILAR VOLUMES

Products of Free Groups in the Unit Grou
Products of Free Groups in the Unit Group of Integral Group Rings
✍ Eric Jespers; Guilherme Leal; Angel del Rı́o 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 253 KB

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

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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

This paper deals with the isomorphism problem for integral group rings of infinite groups. In the first part we answer a question of Mazur by giving conditions for the isomorphism problem to be true for integral group rings of groups that are a direct product of a finite group and a finitely generat