Block Fusion Systems and the Center of the Group Ring

Publikation: Bog/antologi/afhandling/rapportPh.d.-afhandling

  • Martin Wedel Jacobsen
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.
OriginalsprogEngelsk
ForlagDepartment of Mathematical Sciences, Faculty of Science, University of Copenhagen
Antal sider47
StatusUdgivet - 2014

ID: 123060697