The structure of automorphic loops

DOI10.1090/tran/6622zbMath1359.20038arXiv1210.1642OpenAlexW1536916848MaRDI QIDQ2822724

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Publication date: 4 October 2016

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1210.1642

zbMATH Keywords

Lie ringCauchy theoremprimitive groupodd order theoremLagrange theoremBruck loopinner mappingautomorphic loopdihedral automorphic loopmiddle nuclear extensionsimple automorphic loopsolvable loop

Mathematics Subject Classification ID

Loops, quasigroups (20N05)

Related Items (13)

Bol loops and Bruck loops of order \(pq\) up to isotopism ⋮ Lie's correspondence for commutative automorphic formal loops ⋮ Commutator theory for loops. ⋮ Half-isomorphisms of automorphic loops ⋮ Nilpotency in automorphic loops of prime power order. ⋮ Half-isomorphisms of Moufang loops. ⋮ Lie automorphic loops under half-automorphisms ⋮ Abelian extensions and solvable loops. ⋮ Half-isomorphisms of dihedral automorphic loops ⋮ Nuclear properties of loop extensions ⋮ Enumeration of involutory latin quandles, Bruck loops and commutative automorphic loops of odd prime power order ⋮ Basarab loop and the generators of its total multiplication group ⋮ On the structure of the automorphism group of certain automorphic loop

Uses Software

• GAP
• Prover9
• Mace4
• LOOPS

Cites Work

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• On the multiplication group of a loop
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• The structure of commutative automorphic loops
• Searching for small simple automorphic loops
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• A Theorem on A-Loops
• Modified Edgeworth and Cornish-Fisher Expansions with Unknown Cumulants and no Singularities
• Finite Bol loops
• COMMUTATIVE AUTOMORPHIC LOOPS OF ORDER p³
• ALL AUTOMORPHIC LOOPS OF ORDER p² FOR SOME PRIME p ARE ASSOCIATIVE
• Quasigroups. I

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