On the compatibility of planar and nonplanar involutions in translation planes
It is well known that in translation planes of odd order \(p^ r\) affine elations and Baer p-collineations cannot exist simultaneously. In translation planes of even order, elations and Baer involutions can simultaneously exist. Most of such known planes are derivable. The author considers derivable translation planes of even order admitting both elations and Baer involutions that fix the derivable net. He discusses in detail two incompatibility conjectures: I. A derivable translation plane cannot simultaneously admit two nontrivial elations with the same axis and two nontrivial Baer involutions with the same Baer axis that fix a derivable net. II. Let \(\pi\) be a derivable translation plane of even order admitting an elation group of order \(\geq 4\) that fixes a derivable net. Then the full collineation group of the derived plane \({\bar \pi}\) is the group inherited from \(\pi\) (that is, leaves the associated derivable net invariant).
scientific article; zbMATH DE number 3855860
scientific article