Factorization of epimorphisms between projective planes (Q1077710)

Let \(\varphi: \Pi\to\Pi'\) be an epimorphism between projective planes. The author proves that the congruence relations between \(\Pi\) and \(\Pi'\) are linearly ordered. He also characterizes those congruence relations \(\tau\) for which \(\Pi/\tau\) is a projective plane and those for which \(\Pi/\tau\) is a projective Hjelmslev plane. In case \(\Pi\) and \(\Pi'\) are Desarguesian and if \(\varphi\) cannot be properly factored to yield a projective plane between \(\Pi\) and \(\Pi'\), the author proves that any proper factorization of \(\varphi\) yields a Hjelmslev plane as intermediate image.