Spherical space forms—Homotopy types and self-equivalences for the groups Z/a⋊Z/b and Z/a⋊(Z/b×Q2i)

Let G be a finite group one of the forms given in the title with period 2d and X(n) an n-dimensional CW-complex with the homotopy type of an n-sphere. dy the automorphism group Aut(G) to compute the number of distinct homotopy types of spherical space forms with respect to G-actions on all CW-complexes X(2dn−1). At the end, the groups E(X(2dn−1)/γ) of self homotopy equivalences of space forms X(2dn−1)/γ associated with free and cellular G-actions γ on X(2dn−1) are determined.