Resolution of a family of Galois embedding problems with cyclic kernel

Abstract

In this paper we compute the obstruction and the solutions of cyclic embedding problems given by $$ (E): \quad 0 \rightarrow \mathbb{Z}/n\mathbb{Z} \rightarrow E \rightarrow \Gamma=\mathbb{Z}/n\mathbb{Z} \times \stackrel{m)}{\cdots} \times \mathbb{Z}/n\mathbb{Z} \rightarrow 0 , $$ with $\mathbb{Z}/n\mathbb{Z}$ trivial $\Gamma$-modulo, finding adequate representations of $\Gamma$ in the automorphisms group of a generalized Clifford algebra.