The Non-Abelian Tensor Square of Finite Metacyclic Groups

In this paper, we investigate the group $\nu (G)$, an extension of the non-abelian tensor square $G$ by the direct product $G\times G$, in order to determine a presentation of $G\otimes G$ when $G$ is a general finite metacyclic group, $G=g(a,b;m,n,r,s)$, with $m$ odd. A presentation of $\nu (G)$ is obtained from that of $G$ and, consequently, we describe the appropriate relevant sections of $\nu (G)$, such as the non-abelian tensor square, the exterior square $G\wedge G$ and the Schur multiplier, $M(G)$.