Multiplication groups of commutative automorphic \(p\)-loops of odd order are \(p\)-groups.

DOI10.1016/J.JALGEBRA.2011.09.038zbMath1250.20059OpenAlexW2077150039MaRDI QIDQ420710

Piroska Csörgő

Publication date: 23 May 2012

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

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2011.09.038

zbMATH Keywords

centertranslationscentral nilpotenceinner mapping groupsmultiplication groupsA-loopscommutative automorphic loopsfinite loopsconnected transversals

Mathematics Subject Classification ID

Loops, quasigroups (20N05) Finite nilpotent groups, (p)-groups (20D15)

Related Items (4)

Solvability of commutative automorphic loops ⋮ All finite automorphic loops have the elementwise Lagrange property. ⋮ Nilpotency in automorphic loops of prime power order. ⋮ The structure of automorphic loops

Cites Work

• Unnamed Item
• Nilpotency in automorphic loops of prime power order.
• 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
• Quasigroups. I

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