Group rings and their augmentation ideals

The aim of this article is to lead the reader on a journey through the representation theory of finite groups of Lie type and Hecke algebras. We will present some basic results obtained in recent years, explain the ideas behind them, and give lots of examples; proofs are usually omitted but we provide explicit references to an extensive bibliography.

Computational Aspects of the Isomorphism Problem

Groups St Andrews 2005: The modular isomorphism problem for finite p -groups with a cyclic subgroup of index p2

The modular group algebra problem for small $p$-groups of maximal class

Let G be a 2-group of order 2^n, n>5, and nilpotency class n-2. The invariants of such groups determined by their group algebras over the field of two elements are given in the paper.

On 2-groups of almost maximal class

We show that p-groups of order p 5 are determined by their group algebras over the field of p elements. Many cases have been dealt with in earlier work of ourselves and others. The only case whose details remain to be given here is that of groups of nilpotency class 3 for p odd.

/pdf/the-modular-group-algebra-problem-for-groups-of-order-p5-2ryhjatizu.pdf

The modular group algebra problem for groups of order p5

/pdf/the-unit-group-of-the-modular-small-group-algebra-dj60wy84n2.pdf

The Unit Group of the Modular Small Group Algebra

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The modular group algebra problem for small $p$-groups of maximal class

The modular group algebra problem for groups of order p5

The Unit Group of the Modular Small Group Algebra