Linear Methods and Soluble Groups

  • Bertram Huppert
  • Norman Blackburn
Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 242)


Linear methods have been used extensively for quantitative investigations of soluble groups; for soluble linear groups, bounds in terms of the degree are known for such invariants as the order, derived length, etc. In 1956, P. Hall and G. Higman developed these ideas to obtain upper bounds for the p-length of a p-soluble group G in terms of various invariants of the Sylow p-subgroup of G. There emerged from this a body of techniques which have come to be known as Hall-Higman methods. The present chapter is an introduction to these methods. They are given in an elementary form in § 1, which is already sufficient to solve the restricted Burnside problem of exponent 6.


Normal Subgroup Linear Method Prime Divisor Minimum Polynomial Minimal Normal Subgroup 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1982

Authors and Affiliations

  • Bertram Huppert
    • 1
  • Norman Blackburn
    • 2
  1. 1.Mathematisches Institut der UniversitätMainzGermany
  2. 2.Department of MathematicsThe UniversityGB-ManchesterUK

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