Above Isaacs' Head Characters
Abstract
The proof of the inductive McKay condition has been shown to imply that the character theory above the characters of degree not divisible by $p$ of a normal subgroup is locally determined. In this note, we establish a similar result for the Isaacs' head characters of a normal solvable subgroup of an arbitrary group. In particular, we give a new lower bound of the number of conjugacy classes of a finite group in terms of the Carter subgroups of any of its normal solvable subgroups.
Fields of Study & Subjects
Finite Group Theory Research
Advanced Combinatorial Mathematics
Advanced Algebra and Geometry
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 13 February 2026
- Language
- EN
- Document type
- Preprint