The Moufang loops of order 64 and 81.

DOI10.1016/j.jsc.2007.06.004zbMath1131.20053arXiv1509.05700OpenAlexW2161755045MaRDI QIDQ2470061

Petr Vojtěchovský, Gábor P. Nagy

Publication date: 13 February 2008

Published in: Journal of Symbolic Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1509.05700

zbMATH Keywords

GAPnonassociative Moufang loopsclassification of Moufang loopscode loops2-loopsMoufang loops of order 64Moufang loops of order 81

Mathematics Subject Classification ID

Loops, quasigroups (20N05)

Related Items

Moufang loops of odd order \(p^4q^3\), Certain numerical results in non-associative structures, Computing generating sets of minimal size in finite algebras, On abelian-by-cyclic Moufang loops, The geometry of point reflections and quasigroups, A series of algebras generalizing the octonions and Hurwitz-Radon identity, Closest multiplication tables of groups, Unnamed Item, Unnamed Item, Product rules and classification of nonassociative Moufang loops of order 81, On the non-commuting graph in finite Moufang loops, Code loops in dimension at most \(8\), CLASSIFICATION OF MINIMAL NONASSOCIATIVE MOUFANG LOOPS OF ORDER pq³, Code loops in both parities, Enumeration of nilpotent loops via cohomology., Constructions of Commutative Automorphic Loops, Distributive and trimedial quasigroups of order 243, Unnamed Item, Nuclear properties of loop extensions, Enumeration of involutory latin quandles, Bruck loops and commutative automorphic loops of odd prime power order, Unnamed Item, ON GENERALIZED RELATIVE COMMUTATIVITY DEGREE OF FINITE MOUFANG LOOP

Uses Software

• GAP
• LOOPS

Cites Work

• Toward the classification of Moufang loops of order 64.
• On nilpotent Moufang loops with central associators.
• Direct construction of code loops.
• A simple construction for the Fischer-Griess monster group
• Code loops
• Combinatorial polarization
• Moufang loops of odd order \(p^ \alpha q_ 1^ 2\cdots q_ n^ 2r_ 1\cdots r_ m\)
• Moufang loops of odd order \(pq^3\)
• Nilpotency conditions for finite loops
• On loops of odd order. II
• Nilpotence of finite Moufang 2-loops
• Commutative Moufang loops and distributive groupoids of small orders
• Moufang loops of small order
• Moufang loops of class 2 and cubic forms
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