## Abstract

Let G(H) be the monoid of H equivariant self maps of S(nV), the unit sphere of n copies of a finite dimension orthogonal representation V of a finite group H, stabilized over n in an appropriate way. Let SG(H) be the submonid of G(H) consisting of all degree 1 maps. If H_{1} is a subgroup of H there is a natural forgetful map SG(H) → SG(H_{1}) and if Z is the center of H there is a natural action map BZ × SG(H) → SG(H) induced by the natural action of Z on H. The main results of this paper are the calculations of the Hopf algebra structures of H_{*}(SG(Z/p^{n}), Z/p) and H_{*}(BSG(Z/p^{n}), Z/p) for all n and all primes p, the calculations in homology of forgetful maps induced by the natural inclusions Z/p^{n-1} → Z/p^{n} and, for H = Z/2, the calculation of the action map H_{*}(R P^{∞}, Z/2) ⊗ H_{*}(BSG(Z/2), Z/2) → H_{*} (BSG(Z/2), Z/2).

Original language | English (US) |
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Pages (from-to) | 327-377 |

Number of pages | 51 |

Journal | Pacific Journal of Mathematics |

Volume | 108 |

Issue number | 2 |

DOIs | |

State | Published - Oct 1983 |

## ASJC Scopus subject areas

- General Mathematics