| eBook ISBN: | 978-1-4704-0452-9 |
| Product Code: | MEMO/180/848.E |
| List Price: | $65.00 |
| MAA Member Price: | $58.50 |
| AMS Member Price: | $39.00 |
| eBook ISBN: | 978-1-4704-0452-9 |
| Product Code: | MEMO/180/848.E |
| List Price: | $65.00 |
| MAA Member Price: | $58.50 |
| AMS Member Price: | $39.00 |
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 180; 2006; 102 ppMSC: Primary 55; Secondary 20
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.
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Table of Contents
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Chapters
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Introduction
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1. Higher limits over orbit categories
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2. Reduction to simple groups
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3. A relative version of $\Lambda $-functors
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4. Subgroups which contribute to higher limits
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5. Alternating groups
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6. Groups of Lie type in characteristic two
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7. Classical groups of Lie type in odd characteristic
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8. Exceptional groups of Lie type in odd characteristic
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9. Sporadic groups
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10. Computations of $\lim ^1(\mathcal {Z}_G)$
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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.
-
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 $\lim ^1(\mathcal {Z}_G)$
