The structure of commutative automorphic loops

DOI10.1090/S0002-9947-2010-05088-3zbMath1215.20060arXiv0810.1065OpenAlexW2017284704MaRDI QIDQ3082360

Přemysl Jedlička, Petr Vojtěchovský, Michael K. Kinyon

Publication date: 10 March 2011

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

Full work available at URL: https://arxiv.org/abs/0810.1065

zbMATH Keywords

groupscommutative Moufang loopsquasigroupsinner mappingsautomorphic loopscommutative A-loopsloops of odd order

Mathematics Subject Classification ID

Loops, quasigroups (20N05)

Related Items (16)

Incidence properties of cosets in loops ⋮ Lie's correspondence for commutative automorphic formal loops ⋮ Cycle structure of autotopisms of quasigroups and latin squares ⋮ Solvability of commutative automorphic loops ⋮ All finite automorphic loops have the elementwise Lagrange property. ⋮ Nilpotency in automorphic loops of prime power order. ⋮ Multiplication groups of commutative automorphic \(p\)-loops of odd order are \(p\)-groups. ⋮ Lie automorphic loops under half-automorphisms ⋮ COMMUTATIVE AUTOMORPHIC LOOPS OF ORDER p³ ⋮ A Class of Loops Categorically Isomorphic to Bruck Loops of Odd Order ⋮ ALL AUTOMORPHIC LOOPS OF ORDER p² FOR SOME PRIME p ARE ASSOCIATIVE ⋮ NUCLEAR SEMIDIRECT PRODUCT OF COMMUTATIVE AUTOMORPHIC LOOPS ⋮ MULTIPLICATION GROUPS AND INNER MAPPING GROUPS OF CAYLEY–DICKSON LOOPS ⋮ The structure of automorphic loops ⋮ Enumeration of involutory latin quandles, Bruck loops and commutative automorphic loops of odd prime power order ⋮ Automorphic loops and metabelian groups

Uses Software

• Prover9

Cites Work

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• On loops of odd order
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• Constructions of Commutative Automorphic Loops
• A Theorem on A-Loops
• On Nuclearly Nilpotent Loops of Finite Exponent
• Near subgroups of finite groups
• Quasigroups. II

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