On epimorphisms and projectivities of projective planes (Q1841868)

Let \(\varphi :\Pi \rightarrow \Pi '\) be an epimorphism of projective planes mapping the line \(L\) of \(\Pi \) onto \(L'\). In the present paper, the author studies the group \(\mathcal{G}^{\varphi }\) of permutations of \(L'\), induced by the projectivities of \(L\) via \(\varphi \). Geometric characterizations of epimorphisms which stem from uniform valuations having an abelian value group (``friendly epimorphisms'') are provided. If \(\Pi'\) is pappian, both extremal cases for \(\mathcal{G}^{\varphi }\) can be obtained: the group of projectivities of \(L'\) (if \(\varphi \) is ``very friendly''), and the full symmetric group on the lines of \(L'\).