ABSTRACT
We now list the known finite chains of reguli. The possible collineation groups are determined by L.M. Abatangelo [4].
Theorem 64.1. (L.M. Abatangelo [4]). Let pi be a translation plane obtained
from a Desarguesian plane by (q+3)2 -nest replacement. Let G denote the full translation complement and K∗ the kernel homology group of order q − 1. Then G/K∗
contains a subgroup N of index ≤ 4 with the following properties: (1) N is isomorphic either to A4, S4 or A5, or (2) N is dihedral or cyclic with order bounded by a function of q (the complete
bound is also given).
