Results 231 to 240 of about 1,277,019 (268)

Alternating units as free factors in the group of units of integral group rings

Proceedings of the Edinburgh Mathematical Society, 2011
AbstractLet G be a group of odd order that contains a non-central element x whose order is either a prime p ≥ 5 or 3l, with l ≥ 2. Then, in $\mathcal{U}(\mathbb{Z}G)$, the group of units of ℤG, we can find an alternating unit u based on x, and another unit v, which can be either a bicyclic or an alternating unit, such that for all sufficiently large ...
Gonçalves, Jairo Z., Veloso, Paula M.
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The unit group of \(FS_3\).

2007
Summary: We give a complete characterization of the unit group \(\mathcal U(FS_3)\) of the group algebra \(FS_3\) of the symmetric group \(S_3\) of degree 3 over a finite field \(F\). Moreover, over the prime fields \(\mathbb{Z}_2\) and \(\mathbb{Z}_3\), presentations of the unit groups of the group algebras \(\mathbb{Z}_2S_3\) and \(\mathbb{Z}_3S_3 ...
Sharma, R. K., Srivastava, J. B., Manju Khan, Manju   +2 more
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The Ideal Class Group and the Unit Group

1977
Recall that the ideal class group of a number ring R consists of equivalence classes of nonzero ideals under the relation $$ I\sim J\quad iff\quad \alpha I = \beta J\quad for{\text{ }}some{\text{ }}non{\text{ }}zero{\text{ }}\alpha ,\beta \in R; $$ the group operation is multiplication defined in the obvious way, and the fact that this is ...
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Units in Group Algebras of Finite p-Groups

Journal of Mathematical Sciences, 2003
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Bovdi, Adalbert, Patay, Zoltán
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Unit Groups of Group Rings

1999
For a commutative ring R with identity and an arbitrary group G, let RG denote the group ring of G over R and U(RG) its group of units. It is of interest, see the survey by Dennis (1977), to determine the necessary and sufficient conditions on R and G in order that U(RG) has a specific group-theoretic property, e.g., solvability, nilpotence, etc ...
Ashwani K. Bhandari, I. B. S. Passi
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ON THE DERIVED LENGTH OF THE GROUP OF UNITS OF A GROUP ALGEBRA

Journal of Algebra and Its Applications, 2007
Let G be a group with cyclic derived subgroup of p-power order (p > 2), and F a field of characteristic p. We determine the derived length of the group of units of the group algebra FG.
Balogh, Zsolt, Li, Yuanlin
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On the derived length of the unit group of a group algebra

Journal of Group Theory, 2010
Let \(KG\) be the group algebra of the torsion nilpotent group \(G\) over the field \(K\) of positive charateristic \(p\) with the unit group \(U(KG)\) solvable. Conditions under which the unit group is solvable were investigated by several authors in various cases, but little is known about the derived length of the unit group. \textit{C.
CATINO, Francesco, Ernesto SPINELLI
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Group Identities on Units and Symmetric Units of Group Rings

2010
Group Identities on Units of Group Rings.- Group Identities on Symmetric Units.- Lie Identities on Symmetric Elements.- Nilpotence of ...
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The unit group of the modular small group algebra

Mathematical Journal of Okayama University, 1995
Let \(G\) be a finite \(p\)-group whose commutator subgroup is elementary Abelian and \(F\) be the field of \(p\) elements. Denote by \(FG\) the group ring and by \(I(G)\) the kernel of the augmentation mapping. Denote by \(G_2\) the commutator subgroup of \(G\).
Salim, Mohamed A.M., Sandling, Robert
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BASS CYCLIC UNITS AS FACTORS IN A FREE GROUP IN INTEGRAL GROUP RING UNITS

International Journal of Algebra and Computation, 2011
Marciniak and Sehgal showed that if u is a non-trivial bicyclic unit of an integral group ring then there is a bicyclic unit v such that u and v generate a non-abelian free group. A similar result does not hold for Bass cyclic units of infinite order based on non-central elements as some of them have finite order modulo the center.
Jairo Z. Gonçalves, Ángel del Río
openaire   +1 more source