arXiv subjects
Publications and source records attributed to L. Batista de Oliveira.
In this article, we show explicitly the Wedderburn decomposition of the metacyclic group algebra $\mathbb F_qG$, where $G$ has a cyclic subgroup of index 2 and $\gcd(|G|,q)=1$. We also construct the complete set of central and left idempotents of these group algebras.
Let $\mathbb F_q$ be a finite field and $n$ a positive integer. In this article, we prove that, under some conditions on $q$ and $n$, the polynomial $x^n-1$ can be split into irreducible binomials $x^t-a$ and an explicit factorization into irreducible factors is given. Finally, weakening one of our hypothesis, we also obtain factors of the form $x^{2t}-ax^t+b$ and explicit splitting of $x^n-1$ into irreducible factors is given.