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Restriction of p'-degree characters, fields of values, and relative normal complements

  • David Cabrera-Berenguer
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Abstract

Let G be a finite p-solvable group for a prime p, and let P be a Sylow p-subgroup of G. Centella and Navarro proved that there is a canonical bijection Irrp'(Φ1G)→Irrp'(Φ1NG(P)) preserving fields of values, where Φ1G denotes the principal projective indecomposable character of G. In the spirit of a result of Berkovich on the McKay bijection, we characterize when this projective correspondence can be realized by restriction, proving that it holds if and only if NG(P) admits a certain relative normal complement in G. More generally, we establish a refined criterion incorporating fields of values, and we extend this characterization to π-separable groups with nilpotent Hall π-subgroups.

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Cite

BibTeXRIS
BibTeX
@misc{cabreraberenguer2026restriction,
  title = {{Restriction of $p'$-degree characters, fields of values, and relative normal complements}},
  author = {David Cabrera-Berenguer},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.29672},
  eprint = {2610.29672},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.29672},
}
RIS
TY  - UNPB
TI  - Restriction of p'-degree characters, fields of values, and relative normal complements
AU  - David Cabrera-Berenguer
PY  - 2026
DA  - 2026/10/21
PB  - arXiv
DO  - 10.48550/arxiv.2610.29672
UR  - https://arxiv.org/abs/2610.29672
AB  - Let G be a finite p-solvable group for a prime p, and let P be a Sylow p-subgroup of G. Centella and Navarro proved that there is a canonical bijection Irr_p'(Φ_1_G)→Irr_p'(Φ_1_N_G(P)) preserving fields of values, where Φ_1_G denotes the principal projective indecomposable character of G. In the spirit of a result of Berkovich on the McKay bijection, we characterize when this projective correspondence can be realized by restriction, proving that it holds if and only if N_G(P) admits a certain relative normal complement in G. More generally, we establish a refined criterion incorporating fields of values, and we extend this characterization to π-separable groups with nilpotent Hall π-subgroups.
ER  -