Publication details
Character tables and defect groups
Abstract
Let B be a block of a finite group G with defect group D. We prove that the exponent of the center of D is determined by the character table of G. In particular, we show that D is cyclic if and only if B contains a “large” family of irreducible p-conjugate characters. More generally, for abelian D we obtain an explicit formula for the exponent of D in terms of character values. In small cases even the isomorphism type of D is determined in this situation. Moreover, it can read off from the character table whether |D/D′|=4 where D′ denotes the commutator subgroup of D. We also propose a new characterization of nilpotent blocks in terms of the character table.
Details
- Organisation(s)
-
Institute of Algebra, Number Theory and Discrete Mathematics
- Type
- Article
- Journal
- Journal of algebra
- Volume
- 562
- Pages
- 323-340
- No. of pages
- 18
- ISSN
- 0021-8693
- Publication date
- 15.11.2020
- Publication status
- Published
- Peer reviewed
- Yes
- ASJC Scopus subject areas
- Algebra and Number Theory
- Electronic version(s)
-
https://doi.org/10.48550/arXiv.2007.04919 (Access:
Open
)
https://doi.org/10.1016/j.jalgebra.2020.05.040 (Access: Closed )
