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Whitehead Groups of Integral Group Rings

Whitehead Groups of Integral Group Rings
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UNIPOTENT GROUP SCHEMES OVER INTEGRAL RINGS

Mathematics of the USSR-Izvestiya, 1974
In this paper we study families of unipotent algebraic groups over integral rings. The main results relate to the geometry of such families. In particular, we prove that, under some hypotheses, the space of such a family is isomorphic to an affine space over the base.
Veĭsfeĭler, B. Yu., Dolgachev, I. V.
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Graded Reversibility in Integral Group Rings

Acta Applicandae Mathematicae, 2008
A ring is said to be reversible if \(ab=0\) implies \(ba=0\) for ring elements \(a\) and \(b\). Reversible rings were studied by \textit{P. M. Cohn} [Bull. Lond. Math. Soc. 31, No. 6, 641-648 (1999; Zbl 1021.16019)], reversible group rings by \textit{M. Gutan} and \textit{A. Kisielewicz} [J. Algebra 279, No. 1, 280-291 (2004; Zbl 1068.16033)]. Inspired
Li, Yuanlin, Parmenter, M. M.
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Integral Group Rings Without Proper Units

Canadian Mathematical Bulletin, 1987
AbstractIf A is an elementary abelian ρ-group and C one of its cyclic subgroups, the integral group rings ZA contains, of course, the ring ZC. It will be shown below, for A of rank 2 and ρ a regular prime, that every unit of ZA is a product of units of ZC, as C ranges over all cyclic subgroups.
Hoechsmann, K., Sehgal, S. K.
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Finite Subgroups in Integral Group Rings

Canadian Journal of Mathematics, 1996
AbstractA p-subgroup version of the conjecture of Zassenhaus is proved for some finite solvable groups including solvable groups in which any Sylow p-subgroup is either abelian or generalized quaternion, solvable Frobenius groups, nilpotent-by-nilpotent groups and solvable groups whose orders are not divisible by the fourth power of any prime.
Dokuchaev, Michael A., Juriaans, Stanley O.   +1 more
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Integral Group Rings of Finite Groups

Canadian Mathematical Bulletin, 1967
The main object of this paper is to show that the existence of a particular kind of isomorphism between the integral group rings of two finite groups implies that the groups themselves are isomorphic. The proof employs certain types of linear forms which are first discussed in general.
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UNITARY UNITS IN INTEGRAL GROUP RINGS

Journal of Algebra and Its Applications, 2006
Let \(\mathbb{Z} G\) be the integral group ring of a finite group \(G\) and let \(U(\mathbb{Z} G)\) be the group of normalized units of \(\mathbb{Z} G\). The anti-automorphism \(\psi\) of \(G\) is extended to \(\mathbb{Z} G\) and it is defined \(U_\psi(\mathbb{Z} G)=\{u\in U(\mathbb{Z} G)\mid u\psi(u)=1\}\).
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Integral Group Rings of Some p-Groups

Canadian Journal of Mathematics, 1982
1. Introduction. The group of units, , of the integral group ring of a finite non-abelian group G is difficult to determine. For the symmetric group of order 6 and the dihedral group of order 8 this was done by Hughes-Pearson [3] and Polcino Milies [5] respectively.
Ritter, Jürgen, Sehgal, Sudarshan K.
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Units of Integral Group Rings of Some Metacyclic Groups

Canadian Mathematical Bulletin, 1994
AbstractIn this paper, we consider all metacyclic groups of the type 〈a,b | an - 1, b2 = 1, ba = aib〉 and give a concrete description of their rational group algebras. As a consequence we obtain, in a natural way, units which generate a subgroup of finite index in the full unit group, for almost all such groups.
Jespers, Eric, Leal, Guilherme, Polcino Milies, C.   +2 more
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Units in Integral Group Rings of Some Metacyclic Groups

Canadian Mathematical Bulletin, 1987
AbstractLet p be odd prime and suppose that G = 〈a, b〉 where ap-1 = bp = 1, a-1 ba = br, and r is a generator of the multiplicative group of integers mod p. An explicit characterization of the group of normalized units V of the group ring ZG is given in terms of a subgroup of GL(p - 1, Z).
Allen, P. J., Hobby, C.
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