Publication details
Groups of p-central type
- authored by
- Benjamin Sambale
- Abstract
A finite group G with center Z is of central type if there exists a fully ramified character λ∈ Irr (Z) , i. e. the induced character λG is a multiple of an irreducible character. Howlett–Isaacs have shown that G is solvable in this situation. A corresponding theorem for p-Brauer characters was proved by Navarro–Späth–Tiep under the assumption that p≠ 5 . We show that there are no exceptions for p= 5 , i. e. every group of p-central type is solvable. Gagola proved that every solvable group can be embedded in G/Z for some group G of central type. We generalize this to groups of p-central type. As an application we construct some interesting non-nilpotent blocks with a unique Brauer character. This is related to a question by Kessar and Linckelmann.
- Organisation(s)
-
Institute of Algebra, Number Theory and Discrete Mathematics
- Type
- Article
- Journal
- Mathematische Zeitschrift
- Volume
- 306
- No. of pages
- 9
- ISSN
- 0025-5874
- Publication date
- 24.11.2023
- Publication status
- Published
- Peer reviewed
- Yes
- ASJC Scopus subject areas
- General Mathematics
- Electronic version(s)
-
https://doi.org/10.1007/s00209-023-03406-3 (Access:
Open)
