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.
CITATION STYLE
Eick, B., Horn, M., & Hulpke, A. (2018). Constructing groups of ‘small’ order: Recent results and open problems. In Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory (pp. 199–211). Springer International Publishing. https://doi.org/10.1007/978-3-319-70566-8_8
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