**Memoirs of the American Mathematical Society**

2006;
102 pp;
Softcover

MSC: Primary 55;
Secondary 20

Print ISBN: 978-0-8218-3828-0

Product Code: MEMO/180/848

List Price: $65.00

AMS Member Price: $39.00

MAA Member Price: $58.50

**Electronic ISBN: 978-1-4704-0452-9
Product Code: MEMO/180/848.E**

List Price: $65.00

AMS Member Price: $39.00

MAA Member Price: $58.50

# Equivalences of Classifying Spaces Completed at the Prime Two

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*Bob Oliver*

We prove here the Martino-Priddy conjecture at the prime \(2\): the \(2\)-completions of the classifying spaces of two finite groups \(G\) and \(G'\) are homotopy equivalent if and only if there is an isomorphism between their Sylow \(2\)-subgroups which preserves fusion. This is a consequence of a technical algebraic result, which says that for a finite group \(G\), the second higher derived functor of the inverse limit vanishes for a certain functor \(\mathcal{Z}_G\) on the \(2\)-subgroup orbit category of \(G\). The proof of this result uses the classification theorem for finite simple groups.

#### Table of Contents

# Table of Contents

## Equivalences of Classifying Spaces Completed at the Prime Two

- Contents v6 free
- Introduction 18 free
- Chapter 1. Higher limits over orbit categories 613 free
- Chapter 2. Reduction to simple groups 1724
- Chapter 3. A relative version of Λ-functors 2532
- Chapter 4. Subgroups which contribute to higher limits 3239
- Chapter 5. Alternating groups 4148
- Chapter 6. Groups of Lie type in characteristic two 4451
- Chapter 7. Classical groups of Lie type in odd characteristic 5259
- Chapter 8. Exceptional groups of Lie type in odd characteristic 6370
- Chapter 9. Sporadic groups 8491
- Chapter 10. Computations of lim[sup(1)](Z[sub(G)]) 98105
- Bibliography 100107