Constructing groups of ‘small’ order: recent results and open problems. (English) Zbl 1400.20014
Böckle, Gebhard (ed.) et al., Algorithmic and experimental methods in algebra, geometry, and number theory. Cham: Springer (ISBN 978-3-319-70565-1/hbk; 978-3-319-70566-8/ebook). 199-211 (2017).
Summary: 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.
For the entire collection see [Zbl 1394.14002].
For the entire collection see [Zbl 1394.14002].
MSC:
| 20D60 | Arithmetic and combinatorial problems involving abstract finite groups |
| 20D45 | Automorphisms of abstract finite groups |
| 20E22 | Extensions, wreath products, and other compositions of groups |
| 20-04 | Software, source code, etc. for problems pertaining to group theory |
| 20-03 | History of group theory |
| 01A65 | Development of contemporary mathematics |
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