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

DOI10.1007/978-3-319-70566-8_8zbMath1400.20014OpenAlexW2789428764MaRDI QIDQ4556573

Max Horn, Bettina Eick, Alexander Hulpke

Publication date: 16 November 2018

Published in: Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-319-70566-8_8

zbMATH Keywords

algorithmsenumerationdeterminationsmall groups

Mathematics Subject Classification ID

Arithmetic and combinatorial problems involving abstract finite groups (20D60) Development of contemporary mathematics (01A65) Automorphisms of abstract finite groups (20D45) Extensions, wreath products, and other compositions of groups (20E22) Software, source code, etc. for problems pertaining to group theory (20-04) History of group theory (20-03)

Related Items (4)

The enumeration of groups of order \(p^{n}q\) for \(n\leq 5\) ⋮ On the number of groups of order 1024 ⋮ Groups whose orders factorise into at most four primes ⋮ The perfect groups of order up to two million

Uses Software

• GAP
• ANUPQ
• SmallGroups Library
• AutPGrp
• GroupExt
• GrpConst
• SglPPow

Cites Work

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• The construction of finite solvable groups revisited.
• Counting groups: Gnus, Moas, and other exotica
• Construction of finite groups
• Automorphism group computation and isomorphism testing in finite groups
• The \(p\)-group generation algorithm
• Groups and nilpotent Lie rings whose order is the sixth power of a prime.
• The groups with order \(p^7\) for odd prime \(p\).
• THE GROUPS OF ORDER qⁿ· p
• The groups of order at most 2000
• CONSTRUCTING AUTOMORPHISM GROUPS OF p-GROUPS
• A MILLENNIUM PROJECT: CONSTRUCTING SMALL GROUPS

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