Commutators in groups definable in o-minimal structures

Baro, Elías; Jaligot, Eric; Otero, Margarita

doi:10.1090/S0002-9939-2012-11209-2

Commutators in groups definable in o-minimal structures
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by Elías Baro, Eric Jaligot and Margarita Otero PDF

Proc. Amer. Math. Soc. 140 (2012), 3629-3643 Request permission

Abstract:

We prove the definability and actually the finiteness of the commutator width of many commutator subgroups in groups definable in o-minimal structures. This 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.

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