On unit group of a finite local rings with 4-nilpotent radical of Jacobson (Q2403644)

The present paper describes the structure of the unit group of a commutative finite local rings \(R\) of characteristic \(p\) with Jacobson radical \(J\) such that \(\dim_{F}J/J^{2}=2\), \(\dim_{F}J2/J^{3}=2\), \(\dim_{F}J^{3}=1\), \( J^{4}=(0)\) and \(F=R/J\cong GF(p^{r})\), the finite field of \(p^{r}\) elements.