FINITE LOOPS WITH NILPOTENT INNER MAPPING GROUPS ARE CENTRALLY NILPOTENT

DOI10.1017/S0004972708001093zbMath1167.20039OpenAlexW2168805792MaRDI QIDQ3619861

Markku Niemenmaa

Publication date: 9 April 2009

Published in: Bulletin of the Australian Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0004972708001093

zbMATH Keywords

inner mapping groupsconnected transversalscentrally nilpotent loops

Mathematics Subject Classification ID

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

Related Items

Topological loops with decomposable solvable multiplication groups, Bruck Loops with Abelian Inner Mapping Groups, On finite loops with nilpotent inner mapping groups., Commutator theory for loops., A SOLVABILITY CRITERION FOR FINITE LOOPS, Loops with Abelian Inner Mapping Groups: An Application of Automated Deduction, Abelian extensions and solvable loops., On dihedral 2-groups as inner mapping groups of finite commutative inverse property loops, The Multiplication Group of an AG-group, On Finite Nonabelian Loop Capable Groups, Small loops of nilpotency class 3 with commutative inner mapping groups, Moufang loops with commuting inner mappings., On finite commutative IP-loops with elementary abelian inner mapping groups of order $p^5$

Cites Work

• Abelian inner mappings and nilpotency class greater than two.
• On multiplication groups of loops
• Solvable groups and loops
• On connected transversals to Abelian subgroups and loop theoretical consequences.
• Connected transversals to nilpotent groups
• On Connected Transversals to Abelian Subgroups in Finite Groups
• Contributions to the Theory of Loops