A counter example for nilpotent groups

Let R be a ring with 1, I be a nilpotent subring of R (there exists a natural number n, such that I ⁿ = 0), and I be generated by {x _j |j ∈ J} as ring. Write U = 1 + I, and it is a nilpotent group with class ? n?1. Let G be the subgroup of U which is generated by {1+x _j |j ∈ J}. The group constructed in this paper indicates that the nilpotency class of G can be less than that of U.