GROUP ACTIONS ON SPHERES WITH RANK ONE ISOTROPY

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