TY - BOOK

T1 - Block Fusion Systems and the Center of the Group Ring

AU - Jacobsen, Martin Wedel

PY - 2014

Y1 - 2014

N2 - This thesis develops some aspects of the theory of block fusion systems.Chapter 1 contains a brief introduction to the group algebra and some simpleresults about algebras over a field of positive characteristic. In chapter 2we define the concept of a fusion system and the fundamental property ofsaturation. We also define block fusion systems and prove that they aresaturated. Chapter 3 develops some tools for relating block fusion systemsto the structure of the center of the group algebra. In particular, it is proventhat a block has trivial defect group if and only if the center of the blockalgebra is one-dimensional. Chapter 4 consists of a proof that block fusionsystems of symmetric groups are always group fusion systems of symmetricgroups, and an analogous result holds for the alternating groups.

AB - This thesis develops some aspects of the theory of block fusion systems.Chapter 1 contains a brief introduction to the group algebra and some simpleresults about algebras over a field of positive characteristic. In chapter 2we define the concept of a fusion system and the fundamental property ofsaturation. We also define block fusion systems and prove that they aresaturated. Chapter 3 develops some tools for relating block fusion systemsto the structure of the center of the group algebra. In particular, it is proventhat a block has trivial defect group if and only if the center of the blockalgebra is one-dimensional. Chapter 4 consists of a proof that block fusionsystems of symmetric groups are always group fusion systems of symmetricgroups, and an analogous result holds for the alternating groups.

UR - https://soeg.kb.dk/permalink/45KBDK_KGL/1pioq0f/alma99122515910405763

M3 - Ph.D. thesis

BT - Block Fusion Systems and the Center of the Group Ring

PB - Department of Mathematical Sciences, Faculty of Science, University of Copenhagen

ER -