All finite automorphic loops have the elementwise Lagrange property.

DOI10.1216/RMJ-2015-45-4-1101zbMath1334.20060OpenAlexW1891871434MaRDI QIDQ888104

Piroska Csörgő

Publication date: 4 November 2015

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.rmjm/1446472424

zbMATH Keywords

orders of elementsinner mapping groupsmultiplication groupsA-loopsfinite loopsconnected transversalsautomorphic loopselementwise Lagrange property

Mathematics Subject Classification ID

Arithmetic and combinatorial problems involving abstract finite groups (20D60) Loops, quasigroups (20N05)

Related Items (1)

The structure of automorphic loops

Cites Work

• Nilpotency in automorphic loops of prime power order.
• Multiplication groups of commutative automorphic \(p\)-loops of odd order are \(p\)-groups.
• Loops whose inner mappings are automorphisms
• On multiplication groups of loops
• Conjugacy closed loops and their multiplication groups.
• Every diassociative A-loop is Moufang
• Constructions of Commutative Automorphic Loops
• The structure of commutative automorphic loops
• Contributions to the Theory of Loops

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