Classes of free group extensions

Abstract

In this paper we identify different classes of free group extension using core graphs. We show that every free group extension $H\le K\le F$ has a base $B$ such that the associated pointed graph morphism ${\Gamma }_B\left(H\right)\to {\Gamma }_B\left(H\right)$ is onto. But if we examine graphs without base points, there is an extension $⟨b⟩\le ⟨b,ab{a}^{-1}⟩<F_{\left\{a,b\right\}}$ such that for every base of $F_{\left\{a,b\right\}}$ the associated graph morphisms are injective.

arXiv admin note: text overlap with arXiv:1907.00243