The semigroups of order 9 and their automorphism groups.

DOI10.1007/s00233-013-9504-9zbMath1291.20054arXiv1301.6023OpenAlexW1990759531WikidataQ61442790 ScholiaQ61442790MaRDI QIDQ2447225

Andreas Distler, Tom Kelsey

Publication date: 25 April 2014

Published in: Semigroup Forum (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1301.6023

zbMATH Keywords

automorphism groupsfinite semigroupsenumerationsnumbers of semigroups

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Exact enumeration problems, generating functions (05A15) General structure theory for semigroups (20M10) Software, source code, etc. for problems pertaining to group theory (20-04)

Related Items

On groupoids with Bol-Moufang type identities, On join irreducible \(J\)-trivial semigroups, Enumerating transformation semigroups, A survey on varieties generated by small semigroups and a companion website, Enumerating, cataloguing and classifying all quantales on up to nine elements, Minimum degrees of finite rectangular bands, null semigroups, and variants of full transformation semigroups, Enumeration of finite inverse semigroups, Intervals of varieties of involution semigroups with contrasting reduct intervals

Uses Software

• GAP
• OEIS
• Smallsemi
• SmallGroups Library
• MINION
• Semigroups

Cites Work

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• The monoids of orders eight, nine \& ten.
• Die Halbgruppen der Ordnungen \(\leq 7\)
• Semigroups of order \(8\)
• Computing finite commutative semigroups
• Semigroups admitting relative inverses
• The Number of Semigroups of Order n
• Minimal Permutation Representations of Finite Groups
• SWAC Computes 126 Distinct Semigroups of Order 4