Vanishing-set inclusion and character degrees in finite p-groups

@misc{zhang2026vanishingset,
  title = {{Vanishing-set inclusion and character degrees in finite $p$-groups}},
  author = {Zhi-Lin Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.03541},
  eprint = {2611.03541},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.03541},
}

TY  - UNPB
TI  - Vanishing-set inclusion and character degrees in finite p-groups
AU  - Zhi-Lin Zhang
PY  - 2026
DA  - 2026/11/02
PB  - arXiv
DO  - 10.48550/arxiv.2611.03541
UR  - https://arxiv.org/abs/2611.03541
AB  - Let G be a finite p-group and let χ,ψ∈Irr(G). We prove that Van(χ)⊆Van(ψ) Longrightarrow χ(1)|ψ(1), where Van(θ)={g∈ G:θ(g)=0}. Consequently, two irreducible characters of a finite p-group with the same vanishing set have the same degree. This answers a question attributed to J. Sangroniz and recorded by Hung, Moretó, and Morotti, extending the previously known case in which one character has degree p. The same divisibility conclusion holds for irreducible characters of finite nilpotent groups.
ER  -