Results 301 to 310 of about 721,077 (354)
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Integral Group Rings Without Proper Units
Canadian Mathematical Bulletin, 1987AbstractIf 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, 1996AbstractA 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. +1 more
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Integral Group Rings of Finite Groups
Canadian Mathematical Bulletin, 1967The 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, 2006Let \(\mathbb{Z} G\) 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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Units of Integral Group Rings of Some Metacyclic Groups
Canadian Mathematical Bulletin, 1994AbstractIn 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 +2 more
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Units in Integral Group Rings of Some Metacyclic Groups
Canadian Mathematical Bulletin, 1987AbstractLet 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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On hypercentral units in integral group rings
Journal of Group Theory, 2007Let \(G\) be a group. An integral domain of characteristic \(0\) is called \(G\)-adapted if whenever \(G\) has an element of prime order \(p\), then \(p\) is not invertible in \(R\). Let \(R\) be such a \(G\)-adapted ring and let \(U\) be the group of units of the group ring \(RG\). Let \(Z_n(U)\) be the \(n\)-th term of the upper central series of \(U\
Hertweck, M. +3 more
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Integral Group Rings of Finite Groups of Lie Type
Bulletin of the London Mathematical Society, 1999The isomorphism problem for integral group rings, which is the question whether for two groups \(G\) and \(H\), \(\mathbb{Z} G\cong\mathbb{Z} H\) implies \(G\cong H\), is studied for certain finite groups of Lie type. Namely, if \(\mathbb{G}\) is a simply connected simple algebraic group over an algebraically closed field \(k\) of positive ...
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Bicyclic Units in some Integral Group Rings
Canadian Mathematical Bulletin, 1995AbstractA description is given of the unit group for the two groups G = D12 and G = D8 × C2. In particular, it is shown that in both cases the bicyclic units generate a torsion-free normal complement. It follows that the Bass-cyclic units together with the bicyclic units generate a subgroup of finite index in for all n ≥ 3.
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