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

Bettina Eick (), Max Horn () and Alexander Hulpke ()
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Bettina Eick: TU Braunschweig
Max Horn: Justus-Liebig-Universität Gießen
Alexander Hulpke: Colorado State University

A chapter in Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory, 2017, pp 199-211 from Springer

Abstract: 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; 20D45; 20E22; 20-04 (search for similar items in EconPapers)
Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-70566-8_8

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DOI: 10.1007/978-3-319-70566-8_8

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