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Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory pp 199–211Cite as

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

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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.

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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.

Author information

Authors and Affiliations

  1. TU Braunschweig, Pockelsstraße 14, 38106, Braunschweig, Germany

    Bettina Eick

  2. Justus-Liebig-Universität Gießen, Arndtstraße 2, 35392, Gießen, Germany

    Max Horn

  3. Colorado State University, Fort Collins, CO, 80523-1874, USA

    Alexander Hulpke

Authors
  1. Bettina Eick
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  2. Max Horn
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  3. Alexander Hulpke
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Corresponding author

Correspondence to Bettina Eick .

Editor information

Editors and Affiliations

  1. IWR, Heidelberg University, Heidelberg, Germany

    Gebhard Böckle

  2. Department of Mathematics, Technische Universität Kaiserslautern, Kaiserslautern, Germany

    Wolfram Decker

  3. Department of Mathematics, Technische Universität Kaiserslautern, Kaiserslautern, Germany

    Gunter Malle

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Eick, B., Horn, M., Hulpke, A. (2017). Constructing Groups of ‘Small’ Order: Recent Results and Open Problems. In: Böckle, G., Decker, W., Malle, G. (eds) Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory. Springer, Cham. https://doi.org/10.1007/978-3-319-70566-8_8

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