Nilpotency in automorphic loops of prime power order.

DOI10.1016/j.jalgebra.2011.09.034zbMath1250.20061arXiv1011.0982OpenAlexW2962871697MaRDI QIDQ420709

Petr Vojtěchovský, Přemysl Jedlička, Michael K. Kinyon

Publication date: 23 May 2012

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

Full work available at URL: https://arxiv.org/abs/1011.0982

zbMATH Keywords

central nilpotencyA-loopscommutative automorphic loopsfinite loopsprime power order loops

Mathematics Subject Classification ID

Loops, quasigroups (20N05)

Related Items

Solvability of commutative automorphic loops, All finite automorphic loops have the elementwise Lagrange property., Commutator theory for loops., Multiplication groups of commutative automorphic \(p\)-loops of odd order are \(p\)-groups., 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, The structure of automorphic loops, Enumeration of involutory latin quandles, Bruck loops and commutative automorphic loops of odd prime power order

Uses Software

• GAP
• Prover9
• Mace4
• LOOPS

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Multiplication groups of commutative automorphic \(p\)-loops of odd order are \(p\)-groups.
• Loops whose inner mappings are automorphisms
• On the extension of involutorial Bol loops
• On loops of odd order. II
• Nilpotence of finite Moufang 2-loops
• On loops of odd order
• Bemerkungen über die Verteilung der quadratischen Reste
• The structure of automorphic loops
• Constructions of Commutative Automorphic Loops
• The structure of commutative automorphic loops
• Searching for small simple automorphic loops
• COMMUTATIVE AUTOMORPHIC LOOPS OF ORDER p³
• Quasigroups. I