Chapter

Probabilistic Group Theory, Combinatorics, and Computing

Volume 2070 of the series Lecture Notes in Mathematics pp 35-82

Date:

Estimation Problems and Randomised Group Algorithms

  • Alice C. NiemeyerAffiliated withCentre for the Mathematics of Symmetry and Computation, School of Mathematics and Statistics, The University of Western Australia Email author 
  • , Cheryl E. PraegerAffiliated withCentre for the Mathematics of Symmetry and Computation, School of Mathematics and Statistics, The University of Western AustraliaKing Abdulaziz University
  • , Ákos SeressAffiliated withCentre for the Mathematics of Symmetry and Computation, School of Mathematics and Statistics, The University of Western AustraliaThe Ohio State University

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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.