Abstract
This thesis develops some aspects of the theory of block fusion systems.
Chapter 1 contains a brief introduction to the group algebra and some simple
results about algebras over a field of positive characteristic. In chapter 2
we define the concept of a fusion system and the fundamental property of
saturation. We also define block fusion systems and prove that they are
saturated. Chapter 3 develops some tools for relating block fusion systems
to the structure of the center of the group algebra. In particular, it is proven
that a block has trivial defect group if and only if the center of the block
algebra is one-dimensional. Chapter 4 consists of a proof that block fusion
systems of symmetric groups are always group fusion systems of symmetric
groups, and an analogous result holds for the alternating groups.
Chapter 1 contains a brief introduction to the group algebra and some simple
results about algebras over a field of positive characteristic. In chapter 2
we define the concept of a fusion system and the fundamental property of
saturation. We also define block fusion systems and prove that they are
saturated. Chapter 3 develops some tools for relating block fusion systems
to the structure of the center of the group algebra. In particular, it is proven
that a block has trivial defect group if and only if the center of the block
algebra is one-dimensional. Chapter 4 consists of a proof that block fusion
systems of symmetric groups are always group fusion systems of symmetric
groups, and an analogous result holds for the alternating groups.
| Originalsprog | Engelsk |
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| Forlag | Department of Mathematical Sciences, Faculty of Science, University of Copenhagen |
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| Antal sider | 47 |
| Status | Udgivet - 2014 |