Group actions on spheres with rank one isotropy

Abstract

Let G G be a rank two finite group, and let H \mathcal {H} denote the family of all rank one p p -subgroups of G G for which rank p ⁡ ( G ) = 2 \operatorname {rank}_p(G)=2 . We show that a rank two finite group G G which satisfies certain explicit group-theoretic conditions admits a finite G G -CW-complex X ≃ S n X\simeq S^n with isotropy in H \mathcal {H} , whose fixed sets are homotopy spheres. Our construction provides an infinite family of new non-linear G G -CW-complex examples.