The special circulant matrix and units in group rings.
The structure of the unit group of the group algebra
The structure of the unit group of the group algebra of the group over any finite field of characteristic 2 is established in terms of split extensions of cyclic groups.
The unit group of .
The unit groups of semisimple group algebras of some non-metabelian groups of order
We consider all the non-metabelian groups of order that have exponent either or and deduce the unit group of semisimple group algebra . Here, denotes the power of a prime, i.e., for prime and a positive integer . Up to isomorphism, there are groups of order that have exponent either or . Additionally, we also discuss how to simply obtain the unit groups of the semisimple group algebras of those non-metabelian groups of order that are a direct product of two nontrivial...
Torsion units for some almost simple groups
We investigate the Zassenhaus conjecture regarding rational conjugacy of torsion units in integral group rings for certain automorphism groups of simple groups. Recently, many new restrictions on partial augmentations for torsion units of integral group rings have improved the effectiveness of the Luther-Passi method for verifying the Zassenhaus conjecture for certain groups. We prove that the Zassenhaus conjecture is true for the automorphism group of the simple group . Additionally we prove that...
Torsion units in group rings.
Let U(RG) be the unit group of the group ring RG. In this paper we study group rings RG whose support elements of every torsion unit are torsion, where R is either the ring of integers Z or a field K.
Torsion units in integral group rings.
Trivial units in commutative group algebras.
Unit 1-stable range for ideals.
Unit groups of group algebras of some small groups
Let be a group algebra of a group over a field and the unit group of . It is a classical question to determine the structure of the unit group of the group algebra of a finite group over a finite field. In this article, the structure of the unit group of the group algebra of the non-abelian group with order over any finite field of characteristic is established. We also characterize the structure of the unit group of over any finite field of characteristic and the structure of...
Unitary subgroup of integral group rings.
Let A be a finite abelian group and G = A x 〈b〉, b2 = 1, ab = a-1, ∀a ∈ A. We find generators up to finite index of the unitary subgroup of ZG. In fact, the generators are the bicyclic units. For an arbitrary group G, let B2(ZG) denote the group generated by the bicyclic units. We classify groups G such that B2(ZG) is unitary.
Unitary subgroup of integral groups rings.
Unitary units in modular group algebras.
Units in group rings of crystallographic groups
In [3], the authors initiated a technique of using affine representations to study the groups of units of integral group rings of crystallographic groups. In this paper, we use this approach for some special classes of crystallographic groups. For a first class of groups we obtain a normal complement for the group inside the group of normalized units. For a second class of groups we show that the Zassenhaus conjectures ZC1 and ZC3 are valid. This generalizes the results known for the infinite dihedral...
Units of F5kD10
2000 Mathematics Subject Classification: 20C05, 16U60, 16S84, 15A33.The Structure of the Unit Group of the Group Algebra of the group D10 over any field of characteristic 5 is established in terms of split extensions of cyclic groups.
Warfield Invariants in Abelian Group Algebras
Warfield invariants in abelian group rings.
Let R be a perfect commutative unital ring without zero divisors of char(R) = p and let G be a multiplicative abelian group. Then the Warfield p-invariants of the normed unit group V (RG) are computed only in terms of R and G. These cardinal-to-ordinal functions, combined with the Ulm-Kaplansky p-invariants, completely determine the structure of V (RG) whenever G is a Warfield p-mixed group.
Whitehead groups of exchange rings with primitive factors Artinian.
Wreath products in modular group algebras of some finite 2-groups.
Wreath products in the unit group of modular group algebras of 2-groups of maximal class.