Definable nilpotent and soluble envelopes in groups without the independence property
We prove that in a group without the independence property a nilpotent subgroup is always contained in a definable nilpotent subgroup of the same nilpotency class. The analogue for the soluble case is also shown when the subgroup is normal in the ambient group.
definability independence property nilpotent group soluble group msc(2010) 03c45 (0360 20a15)