by Martyn R Dixon (University of Alabama, USA)

This book is concerned with the generalizations of Sylow theorems and the related topics of formations and the fitting of classes to locally finite groups. It also contains details of Sunkov's and Belyaev'ss results on locally finite groups with min-p for all primes p. This is the first time many of these topics have appeared in book form. The body of work here is fairly complete.

• Basic Concepts:
  • Group Theoretical Classes and Closure Operations
  • Radicals and Residuals
  • Local Systems
  • The Minimum Condition and Cernikov Groups
• Sylow Theory in Locally Finite Groups:
  • The Asar-Hartley Theorem for a General Set of Primes
  • Groups with min-p
  • Good Sylow Subgroups
• Groups Satisfying min-p for All Primes p:
  • Sylow Theory in Groups with min-p for All Primes p
  • The 2-Radicable part of a group with min-p for All p
  • The Structure of Groups with min-p for all primes p
• Groups with Conjugate Sylow Subgroups:
  • Upper π-Separable Groups
  • Groups with the Minimum Condition on Centralizers
  • Completely Sylow Integrated Groups
  • Metabelian Groups with min-n
• Sylow Bases in Locally Finite Groups:
  • Sylow Bases in Groups with min-p for All p
  • Co-Hopfian Groups
• Formation Theory in Locally Finite Groups:
  • Locally Defined Formations
• Fitting Classes in Locally Finite Groups:
  • Elementary Properties of Fitting Classes
  • Injectors in Groups with min-p for All Primes p