2005/03/31 by Michael A. Jackson, Jackson, Michael A.
Mathematics · #20C15 #20E15 #55R25 #57Q91 #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.math/0503746
openalex publication_date 2005/03/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we show that most rank two groups act freely on a finite homotopy product of two spheres. This makes new progress on a conjecture by Benson and Carlson which states that a finite group G acts freely on a finite complex with the homotopy type of n spheres if the rank of G is less than or equal to n. Recalling that Qd(p) is the semidirect product of a rank two elementary abelian p-group with SL(2,p), we show that a rank two finite group acts freely on a finite CW-complex homotopic to the product of two spheres if, it does not contain any subquotient isomorphic to Qd(p) for any odd prime p.