Finite unitary ring with minimal non-nilpotent group of units

Let R be a finite unitary ring such that R=R_0[R^*] where R_0 is the prime ring and R^* is not a nilpotent group. We show that if all proper subgroups of R^* are nilpotent groups, then the cardinal of R is a power of prime number 2. In addition, if... Show more