Unit group of algebra of circulant matrices

Abstract

Let $Cr_n(F_p)$ denote the algebra of $n times n$ circulant‎ ‎matrices over $F_p$‎, ‎the finite field of order $p$ a prime‎. ‎The‎ ‎order of the unit groups $mathcal{U}(Cr_3(F_p))$‎, ‎$mathcal{U}(Cr_4(F_p))$ and $mathcal{U}(Cr_5(F_p))$ of algebras of‎ ‎circulant matrices over $F_p$ are computed‎.