Commutators in groups definable in o-minimal structures

2010/06/01 by E. Baro, Baro, E., E. Jaligot +3
Mathematics · #03C60 #03C64 #20A15 #20F12 #20F38 #FOS: Mathematics #Group Theory (math.GR) #Logic (math.LO) #math.GR #math.LO #msc:03C60 #msc:03C64 #msc:20A15 #msc:20F12 #msc:20F38

paper · pdf · doi:10.48550/arxiv.1006.0130

30 pages

arxiv created 2010/06/01 · arxiv updated 2010/06/02

Abstract

We prove the definability, and actually the finiteness of the commutator width, of many commutator subgroups in groups definable in o-minimal structures. It applies in particular to derived series and to lower central series of solvable groups. Along the way, we prove some generalities on groups with the descending chain condition on definable subgroups and/or with a definable and additive dimension.

Related

• Cartan subgroups of groups definable in o-minimal structures
• Solvable groups definable in o-minimal structures
• Groups definable in o-minimal structures: various properties and a diagram
• Groups with Finiteness Conditions on commutator subgroups
• The derived subgroup of linear and simply-connected o-minimal groups