Electronic ISBN:  9781470404529 
Product Code:  MEMO/180/848.E 
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 180; 2006; 102 ppMSC: Primary 55; Secondary 20;
We prove here the MartinoPriddy 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

Chapters

Introduction

1. Higher limits over orbit categories

2. Reduction to simple groups

3. A relative version of $\Lambda $functors

4. Subgroups which contribute to higher limits

5. Alternating groups

6. Groups of Lie type in characteristic two

7. Classical groups of Lie type in odd characteristic

8. Exceptional groups of Lie type in odd characteristic

9. Sporadic groups

10. Computations of $\lim ^1(\mathcal {Z}_G)$


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We prove here the MartinoPriddy 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.

Chapters

Introduction

1. Higher limits over orbit categories

2. Reduction to simple groups

3. A relative version of $\Lambda $functors

4. Subgroups which contribute to higher limits

5. Alternating groups

6. Groups of Lie type in characteristic two

7. Classical groups of Lie type in odd characteristic

8. Exceptional groups of Lie type in odd characteristic

9. Sporadic groups

10. Computations of $\lim ^1(\mathcal {Z}_G)$