Estimation Problems and Randomised Group Algorithms

  • Alice C. Niemeyer
  • Cheryl E. Praeger
  • Ákos Seress
Chapter
Part of the Lecture Notes in Mathematics book series (LNM, volume 2070)

Abstract

This chapter discusses the role of estimation in the design and analysis of randomised algorithms for computing with finite groups.An exposition is given of a variety of different approaches to estimating proportions of important element classes, including geometric methods, and the use of generating functions and the theory of Lie type groups.Numerous results concerning estimation in permutation groups and finite classical groups are surveyed.An application is given to the construction of involution centralisers, a crucial component in the constructive recognition of finite simple groups.

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Copyright information

© Springer-Verlag London 2013

Authors and Affiliations

  • Alice C. Niemeyer
    • 1
  • Cheryl E. Praeger
    • 1
    • 2
  • Ákos Seress
    • 1
    • 3
  1. 1.Centre for the Mathematics of Symmetry and Computation, School of Mathematics and StatisticsThe University of Western AustraliaCrawleyAustralia
  2. 2.King Abdulaziz UniversityJeddahSaudi Arabia
  3. 3.The Ohio State UniversityColumbusUSA

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