turkmath.org

For over a century, the notion of fusion has been of interest by many mathematicians including Burnside, Frobenius and Brauer. Fusion systems were introduced by Puig in the early 1990's. Many results and conjectures in modular representation theory may be interpreted as a statement about fusion systems like Alprein's weight conjecture or Broué's abelian defect group conjecture. There is an important class of fusion systems called saturated fusion systems. It is known that all block fusion systems are saturated. As a generalization of this fact, we work on finding p-permutation group algebras such that the corresponding fusion system becomes saturated.