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Universally extendible characters

  • Benjamin Sambale
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Abstract

Let theta be an ordinary character or a Brauer character of a finite group N. We show that theta extends to every overgroup G=Gθtrianglerighteq N if and only if Z(N) <= Ker(theta) and the deflated character of Inn(N) extends to Aut(N)_theta. This equivalence is compatible with fields of values. A similar investigation for extensions from subnormal subgroups leads to a new characteristic subgroup of N.

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Cite

BibTeXRIS
BibTeX
@misc{sambale2026universally,
  title = {{Universally extendible characters}},
  author = {Benjamin Sambale},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.20520},
  eprint = {2610.20520},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.20520},
}
RIS
TY  - UNPB
TI  - Universally extendible characters
AU  - Benjamin Sambale
PY  - 2026
DA  - 2026/10/14
PB  - arXiv
DO  - 10.48550/arxiv.2610.20520
UR  - https://arxiv.org/abs/2610.20520
AB  - Let theta be an ordinary character or a Brauer character of a finite group N. We show that theta extends to every overgroup G=G_θtrianglerighteq N if and only if Z(N) <= Ker(theta) and the deflated character of Inn(N) extends to Aut(N)_theta. This equivalence is compatible with fields of values. A similar investigation for extensions from subnormal subgroups leads to a new characteristic subgroup of N.
ER  -