Moufang loops with a unique nonidentity commutator (associator, square)

DOI10.1016/0021-8693(90)90087-5zbMath0695.20040OpenAlexW2027508151MaRDI QIDQ909803

Orin Chein, Edgar G. Goodaire

Publication date: 1990

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0021-8693(90)90087-5

zbMATH Keywords

squareassociatorsMoufang loopscommutatorsalternative loop ringscode loops

Mathematics Subject Classification ID

Loops, quasigroups (20N05) Alternative rings (17D05)

Related Items (18)

Autotopisms and Isotopisms of Trilinear Alternating Forms ⋮ On extraspecial left conjugacy closed loops. ⋮ Loop algebras of code loops ⋮ On abelian-by-cyclic Moufang loops ⋮ Minimally nonassociative nilpotent Moufang loops. ⋮ Code loops are RA2 loops ⋮ Variety of loops generated by code loops ⋮ Half-Automorphisms of Cayley–Dickson Loops ⋮ Classification of Osborn loops of order 4n ⋮ (Re)constructing Code Loops ⋮ Code loops in dimension at most \(8\) ⋮ Moufang loops that share associator and three quarters of their multiplication tables. ⋮ Code loops in both parities ⋮ Direct construction of code loops. ⋮ LOOP RINGS SATISFYING IDENTITIES OF BOL–MOUFANG TYPE ⋮ Orthogonal decompositions and canonical embeddings of multilinear alternating forms ⋮ Symmetric multilinear forms and polarization of polynomials ⋮ Integral Loop Rings of Loops Whose Derived Subloop Is Central

Cites Work

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• A simple construction for the Fischer-Griess monster group
• Code loops
• Moufang loops with limited commutativity and one commutator
• Isomorphism of loops which have alternative loop rings
• Loops whose loop rings are alternative
• An "Extra" Law for Characterizing Moufang Loops
• Loops whose loop rings in characteristic 2 are alternative

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