We show that EG × G X N is good whenever X is good and G < Σ N is a finite Abelian permutation p -group. We begin with cyclic permutation groups G [congruent with] [Special characters omitted.] / p n < Σ p n and examine K ( s )*( EG × G [Special characters omitted.] ) via the Atiyah-Hirzebruch-Serre spectral sequence [Special characters omitted.] and the morphisms of spectral sequences [Special characters omitted.] induced from embeddings of G into various wreath products W . Using a strong form of induction we compute a K ( s )*-basis for K ( s )*[Special characters omitted.] and show that [Special characters omitted.] is good. We use these results about [Special characters omitted.] for cyclic p -groups G < Σ p n to establish that EG × G X N is good whenever X is good and G < Σ N is a finite abelian permutation p -group.
My Research
