Soft planes and groups

Abstract

Finite projective planes are constructed using groups that satisfy simple-looking conditions. The resulting projective planes include many known planes and possibly new ones, and are precisely those having a collineation group fixing a flag $(\infty ,L_{\infty })$ and transitive on the flags $(w,W)$ with $w\notin L_{\infty }$ and $\infty \notin W$.

Replaces arXiv:2408.11923v1 with some simpler, shorter proofs and a longer title