Group actions on Spheres with rank one isotropy

Ian Hambleton, Ergun Yalcin

Published 2013-02-03, updated 2014-09-23Version 4

Let G be a rank two finite group, and let $\cH$ denote the family of rank one p-subgroups of G, at all primes where G has p-rank two. We show that a rank two finite group G which satisfies certain group-theoretic conditions admits a finite G-CW-complex X with isotropy in $\cH$, whose fixed sets are homotopy spheres. Our construction provides an infinite family of new non-linear G-CW-complex examples for many of the rank two finite simple groups.