Let G denote the projective special linear group PSL(2, q), for a prime power q. It is shown that a finite 2-subgroup of the group V(ZG) of augmentation 1 units in the integral group ring ZG of G is isomorphic to a subgroup of G. Furthermore, it is shown that a composition factor of a finite subgroup of V(ZG) is isomorphic to a subgroup of G.

That is, a ring of rank n is a ring (commutative, associative, with unit) whose underlying additive group is isomorphic to Z. The prototypical examples of rings of rank n are, of course, orders in degree n number fields. The class of all such examples consists precisely of those rings of rank n that are integral domains. However, there are many interesting examples of rings of rank n that are n...

We calculate the lower Controlled Algebraic K-theory of any finitely generated infinite subgroup of SL(3, Z), the group of 3 × 3 integral matrices of determinant 1.

When a finite group G acts faithfully on a graded integral domain S which is an algebra over a field k, such as a polynomial ring, we consider S as a kG-module. We show that S is asymptotically mostly projective in each degree, and also that it is in fact mostly free in an appropriate sense. Similar results also hold for filtered algebras, such as power series rings.

We classify the finite semigroups S, for which all Z-orders Γ of QS, the unit group U(Γ) is hyperbolic. We also classify the RA-loops L for which the unit loop of its integral loop ring does not contain any free abelian subgroup of rank two.

Cappell’s unitary nilpotent groupsUNil∗(R; R,R) are calculated for the integral group ring R = Z[C2] of the cyclic groupC2 of order two. Specifically, they are determined as modules over the Verschiebung algebra V using the Connolly–Ranicki isomorphism [CR05] and the Connolly–Davis relations [CD04]. 2000 Mathematics Subject Classification: 57R67; 19J25.

In 1996 Jespers and Wang classified finite semigroups whose integral semigroup ring has finitely many units. In a recent paper, Iwaki-Juriaans-Souza Filho continued this line of research by partially classifying the finite semigroups whose rational semigroup algebra contains a Zorder with hyperbolic unit group. In this paper we complete this classification by handling the case in which the semi...

We develop an algorithm for computing numerical evidence for a conjecture whose validity is predicted by the requirement that the Equivariant Tamagawa Number conjectures for Tate motives as formulated by Burns and Flach are compatible with the functional equation of Artin Ä-series. The algorithm includes methods for the computation of Fitting ideals and projective lattices over the integral gro...