
eBook ISBN: | 978-1-4704-0600-4 |
Product Code: | MEMO/209/986.E |
List Price: | $74.00 |
MAA Member Price: | $66.60 |
AMS Member Price: | $44.40 |

eBook ISBN: | 978-1-4704-0600-4 |
Product Code: | MEMO/209/986.E |
List Price: | $74.00 |
MAA Member Price: | $66.60 |
AMS Member Price: | $44.40 |
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 209; 2011; 110 ppMSC: Primary 20; 55
The notion of a fusion system was first defined and explored by Puig, in the context of modular representation theory. Later, Broto, Levi, and Oliver extended the theory and used it as a tool in homotopy theory. The author seeks to build a local theory of fusion systems, analogous to the local theory of finite groups, involving normal subsystems and factor systems. Among other results, he defines the notion of a simple system, the generalized Fitting subsystem of a fusion system, and prove the L-balance theorem of Gorenstein and Walter for fusion systems. He defines a notion of composition series and composition factors and proves a Jordon-Hölder theorem for fusion systems.
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Table of Contents
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Chapters
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Introduction
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1. Background
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2. Direct products
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3. $\mathcal {E}_{1}\wedge \mathcal {E}_{2}$
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4. The product of strongly closed subgroups
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5. Pairs of commuting strongly closed subgroups
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6. Centralizers
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7. Characteristic and subnormal subsystems
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8. $T\mathcal {F}_{0}$
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9. Components
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10. Balance
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11. The fundamental group of $\mathcal {F}^{c}$
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12. Factorizing morphisms
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13. Composition series
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14. Constrained systems
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15. Solvable fusion systems
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16. Fusion systems in simple groups
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17. An example
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The notion of a fusion system was first defined and explored by Puig, in the context of modular representation theory. Later, Broto, Levi, and Oliver extended the theory and used it as a tool in homotopy theory. The author seeks to build a local theory of fusion systems, analogous to the local theory of finite groups, involving normal subsystems and factor systems. Among other results, he defines the notion of a simple system, the generalized Fitting subsystem of a fusion system, and prove the L-balance theorem of Gorenstein and Walter for fusion systems. He defines a notion of composition series and composition factors and proves a Jordon-Hölder theorem for fusion systems.
-
Chapters
-
Introduction
-
1. Background
-
2. Direct products
-
3. $\mathcal {E}_{1}\wedge \mathcal {E}_{2}$
-
4. The product of strongly closed subgroups
-
5. Pairs of commuting strongly closed subgroups
-
6. Centralizers
-
7. Characteristic and subnormal subsystems
-
8. $T\mathcal {F}_{0}$
-
9. Components
-
10. Balance
-
11. The fundamental group of $\mathcal {F}^{c}$
-
12. Factorizing morphisms
-
13. Composition series
-
14. Constrained systems
-
15. Solvable fusion systems
-
16. Fusion systems in simple groups
-
17. An example