My guess that it should not be possible because $SL_2(R)$ would not have a 3-soluble nonnilpotent subgroup. I am not sure whether it is true that any soluble non-nilpotent subgroup would lie in Borel subgroup but I imagine that this is right...
My guess that it should not be possible because $SL_2(R)$ would not have a 3-soluble subgroup. I am not sure whether it is true that any soluble subgroup would lie in Borel subgroup but I imagine that this is right...