Two remarks on Wall's D2 problem

Abstract

If a finite group $G$ is isomorphic to a subgroup of $SO(3)$, then $G$ has the D2-property. Let $X$ be a finite complex satisfying Wall's D2-conditions. If ${\pi }_1(X)=G$ is finite, and $\chi (X)\ge 1-Def(G)$, then $X\vee S^2$ is simple homotopy equivalent to a finite $2$-complex, whose simple homotopy type depends only on $G$ and $\chi (X)$.

9 pages

References in corpus (6)

• Realizing algebraic 2-complexes by cell complexes
• Exotic relation modules and homotopy types for certain 1-relator groups
• The D(2) property for $D_8$
• Quillen's Plus Construction and the D(2) problem
• Minimal algebraic complexes over $D_{4n}$
• Partial Euler Characteristic, Normal Generations and the stable D(2) problem

Cited by in corpus (6)

• On CW-complexes over groups with periodic cohomology
• An exotic presentation of Q_28
• Projective modules and the homotopy classification of $(G,n)$-complexes
• Homotopy classification of 4-manifolds whose fundamental group is dihedral
• 2D problems in groups
• Four-manifolds, two-complexes and the quadratic bias invariant