turkmath.org

In recent work (still in progress) with Ran Levi and Carles Broto, we have been looking at this question, and have found tools for proving that certain fusion systems cannot be realized by linear torsion groups. For example, we showed that if F is a fusion system over a finite p-group and is realized by an infinite linear torsion group, then it is realized by a finite group. We also went through lists of known saturated fusion systems over infinite discrete p-toral groups, and found many examples that are exotic and many that are realizable.