A finite group G with centre Z is of central type if there exists an irreducible character χ such that χ(1)2=|G:Z|. Howlett–Isaacs have shown that such groups are soluble. A corresponding theorem for p-Brauer characters was proved by Navarro–Späth–Tiep under the assumption that p≠5. I have shown that there are no exceptions for p=5. Moreover, I give some applications to p-blocks with a unique Brauer character.
This video was produced by the Okinawa Institute of Science and Technology, as part of their OIST Representation Theory Seminar series.
