Contents

Preface

Biography of D. S. Passman

Group Gradings on Associative Superalgebras

Y.

A. BAHTURIN and

I.

P. SHESTAKOV

Essential Extensions of a Direct Sum of Simple Modules

K.

I.

BEIDAR, S. K. JAIN, and AsHISH K. SRIVASTAVA

Adjoint Actions of Cocommutative Hopf Algebras

JEFFREY BERGEN

Two Statements about Infinite Products that Are Not Quite True

GEORGE M. BERGMAN

Cyclic Structures with Lag-Time Generators

RACHEL BETZ, SANDRAH ECKEL, PETER PAPPAS,

and JENNIFER UYANIK

Central Idempotents in Group Algebras

0.

BROCHE CRISTO and C. POLCINO MILIES

Congruence Subgroups and the Atiyah Conjecture

DANIEL R. FARKAS and PETER

A.

LINNELL

The Adjoint of the Bezoutian

EDWARD FORMANEK

Group Algebras Whose Lie Algebra of Skew-Symmetric Elements Is Nilpotent

vii

ix

1

15

25

35

59

75

89

103

A. GIAMBRUNO and S.

K.

SEHGAL 113

Free Symmetric and Unitary Pairs in Central Simple Algebras with Involution

J. Z. GONQALVES and M. SHIRVANI 121

Orders of Finite Groups of Matrices

RoBERT M. GuRALNICK and MARTIN LORENZ

Passman's Problem on Adjoint Representations

G. HEIDE and A. E. ZALESSKII

On the Modular Isomorphism Problem: Groups of Order 26

MARTIN HERTWECK and MARCOS SORIANO

141

163

177

On the Prime Graph of the Unit Group of Integral Group Rings of Finite Groups

W. KIMMERLE 215

v