Results 231 to 240 of about 10,399,233 (265)
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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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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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UNITARITY OF THE MULTIPLICATIVE GROUP OF AN INTEGRAL GROUP RING
Mathematics of the USSR-Sbornik, 1984A homomorphism of a group into the multiplicative group of the ring of integers is called, in algebraic topology, an orientation homomorphism of the group .If is an element of the integral group ring , we will let denote the element . An element of the multiplicative group is called -unitary if the inverse coincides with or .
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On the Conjugacy Classes in an Integral Group Ring
Canadian Mathematical Bulletin, 1978Let G be a periodic group and ZG its integral group ring. The elements ±g(g∈G) are called the trivial units of ZG. In [1], S. D. Berman has shown that if G is finite, then every unit of finite order is trivial if and only if G is abelian or the direct product of a quaternion group of order 8 and an elementary abelin 2-group. By comparison, Losey in [7]
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Hochschild Cohomology Ring of the Integral Group Ring of the Semidihedral 2-Group
Algebra Colloquium, 2011We determine the ring structure of the Hochschild cohomology HH*(ℤ G) of the integral group ring of the semidihedral 2-group G = SD2rof order 2r.
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Hochschild cohomology ring of the integral group ring of the generalized quaternion group
SUT Journal of Mathematics, 2002Let \(t\) be an integer \(\geq 2\) and \(Q_t\) be the generalized quaternion group, that is: \[ Q_t=\langle x,y\mid x^{2t}=1,\;x^t=y^2,\;yxy^{-1}=x^{-1}\rangle. \] In this paper the author determines the ring structure of the Hochschild cohomology of the group ring \(\mathbb{Z} Q_t\) [see \textit{S. F. Siegel} and \textit{S. J. Witherspoon}, Proc. Lond.
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Free Subgroups in the Unit Groups of Integral Group Rings
Canadian Journal of Mathematics, 1980Let G be a group, ZG the group ring of G over the ring Z of integers, and U(ZG) the group of units of ZG. One method of investigating U(ZG) is to choose some property of groups and try to determine the groups G such that U(ZG) enjoys that property. For example Sehgal and Zassenhaus [9] have given necessary and sufficient conditions for U(ZG) to be ...
Hartley, B., Pickel, P. F.
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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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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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Integral Group Rings of Some p-Groups
Canadian Journal of Mathematics, 19821. 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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