Finite and Locally Finite Groups

This volume contains the proceedings of the NATO Advanced Study Institute on Finite and Locally Finite Groups held in Istanbul, Turkey, 14-27 August 1994, at which there were about 90 participants from some 16 different countries. The ASI received generous financial support from the Scientific Affairs Division of NATO. INTRODUCTION A locally finite group is a group in which every finite set of elements is contained in a finite subgroup. The study of locally finite groups began with Schur's result that a periodic linear group is, in fact, locally finite. The simple locally finite groups are of particular interest. In view of the classification of the finite simple groups and advances in representation theory, it is natural to pursue classification theorems for simple locally finite groups. This was one of the central themes of the Istanbul conference and significant progress is reported herein. The theory of simple locally finite groups intersects many areas of group theory and representation theory, so this served as a focus for several articles in the volume. Every simple locally finite group has what is known as a Kegel cover. This is a collection of pairs {(G , Ni) liE I}, where I is an index set, each group Gi is finite, i Ni

Simple locally finite groups.- Algebraic groups.- Subgroups of simple algebraic groups and related finite and locally finite groups of Lie type.- Finite simple groups and permutation groups.- Finitary linear groups: a survey.- Locally finite simple groups of finitary linear transformations.- Non-finitary locally finite simple groups.- Inert subgroups in simple locally finite groups.- Group rings of simple locally finite groups.- Simple locally finite groups of finite Morley rank and odd type.- Existentially closed groups in specific classes.- Groups acting on polynomial algebras.- Characters and sets of primes for solvable groups.- Character theory and length problems.- Finite p-groups.