Finite unitary ring with minimal non-nilpotent group of units

Mohsen Amiri, Mostafa Amini

Let $R$ be a finite unitary ring such that $R=R_0[R^{\ast }]$ where $R_0$ is the prime ring and $R^{\ast }$ is not a nilpotent group. We show that if all proper subgroups of $R^{\ast }$ are nilpoten…