Four-Dimensional Compact Projective Planes with Collineation Group N6,28

Abstract

We consider a 4-dimensional compact projective plane π = (P, L) whose collineation group σ is 6-dimensional and solvable with a 4-dimensional nilradical N. We assume that σ fixes a flag υ ∈ W, acts transitively on L v \{W}, and fixes no point in the set W{υ}. If π is neither a translation plane nor a dual translation plane, nor a shift plane, then we will show that l(N) ≃ nil × R, i.e. the local structure of N is uniquely determined.