Title: Group actions on Spheres with rank one isotropy
 
Authors: Ian Hambleton and Erg{\" u}n Yal{\c c}{\i}n

Status: submitted.

Address1: 
Department of Mathematics, 
McMaster University,
Hamilton, Ontario L8S 4K1, 
Canada

Email1: hambleton@mcmaster.ca

Address2:
Department of Mathematics, 
Bilkent University,
06800 Bilkent, Ankara, 
Turkey

Email2: yalcine@fen.bilkent.edu.tr 


Abstract: Let $G$ be a rank two finite group, and let $\cH$ denote the family of all rank one $p$-subgroups of $G$, for which  $\rk_p(G)=2$. 
We show that a rank two finite group $G$ which satisfies certain group-theoretic conditions  admits a finite $G$-CW-complex $X\simeq S^n$ with isotropy in $\cH$, whose fixed sets are homotopy spheres.