C. Polcino Milies

Derivations of Upper Triangular Matrix Rings

We give a description of the derivations in Tn(R), the ringof upper triangular matrices over a ring R, assuming only the existence of an identity element. We show that every derivation is the sum of an inner derivation and another one induced from R.

Group algebras of torsion groups and Lie nilpotence

Abstract Let ∗ be an involution of a group algebra FG induced by an involution of the group G. For char F ≠ 2, we classify the torsion groups G with no elements of order 2 whose Lie algebra of ∗-skew elements is nilpotent.

FINITE CONJUGACY IN ALGEBRAS AND ORDERS

Herstein showed that the conjugacy class of a non-central element in the multiplicative group of a division ring is innite. We prove similar results for units in algebras and orders and give applications to group rings.

Finitely Generated Groups G such that G/Z(G) ≈ C p × C p

Finite groups G such that G/Z(G) ≈ C 2 × C 2 where C 2 denotes a cyclic group of order 2 and Z(G) is the center of G were studied in [5] and were used to classify finite loops with alternative loop algebras. In this paper we extend this result to finitely generated groups such that G/Z(G) ≈ C p × C p where C p denotes a cyclic group of prime order p and provide an explicit description of all such groups.

Group rings whose torsion units form a subgroup

In this note, we determine fields K and groups G that are either nilpotent or FC and such that the set of torsion elements of the group ring KG forms a subgroup.

Units of group rings

Abstract In the first part we give a survey of some recent results on constructing finitely many generators for a subgroup of finite index in the unit group of an integral group ring ZG of a finite group G . In the second part we consider the class of indecomposable finite groups G which modulo their center Z ( G ) are a direct product of two copies of the cyclic group C p of odd prime order p . In case Z ( G ) is cyclic, a description of the full unit group is given. In the general case a subgroup of finite index is described.

Cocharacters of group graded algebras and multiplicities bounded by one

Abstract Let G be a finite group and A a G-graded algebra over a field F of characteristic zero. We characterize the -ideals of graded identities of A such that the multiplicities in the graded cocharacter of A are bounded by one. We do so by exhibiting a set of identities of the -ideal. As a consequence we characterize the varieties of G-graded algebras whose lattice of subvarieties is distributive.