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Constructing Groups of ‘Small’ Order: Recent Results and Open Problems

  • Bettina Eick
  • Max Horn
  • Alexander Hulpke
Chapter

Abstract

We investigate the state of the art in the computational determination and enumeration of the groups of small order. This includes a survey of the available algorithms and a discussion of their recent improvements. We then show how these algorithms can be used to determine or enumerate the groups of order at most 20, 000 with few exceptions and we discuss the orders in this range which remain as challenging open problems.

Keywords

Enumeration Determination Small groups Algorithms 

Subject Classifications

20D45 20E22 20-04 

Notes

Acknowledgements

We thank Eamonn O’Brien for comments on drafts of this work. The second author was supported by the DFG Schwerpunkt SPP 1489. The third author was supported by Simons Foundation Collaboration Grant 244502.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2017

Authors and Affiliations

  1. 1.TU BraunschweigBraunschweigGermany
  2. 2.Justus-Liebig-Universität GießenGießenGermany
  3. 3.Colorado State UniversityFort CollinsUSA

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