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PreprintCC BY 4.0arXiv

Elementary divisors of the Cartan matrix for partial characters

  • Kaveh Dastouri
  • Taro Sakurai
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Abstract

Let π be a set of primes and let G be a finite π-separable group. We prove that the Cartan matrix C for the π-partial characters of G is equivalent over the integers to a matrix diag(|CG(x)|π'), where x runs over a set of representatives of the π-classes of G. In particular, we prove that det C = ∏ |CG(x)|π'.

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Cite

BibTeXRIS
BibTeX
@misc{dastouri2026elementary,
  title = {{Elementary divisors of the Cartan matrix for partial characters}},
  author = {Kaveh Dastouri and Taro Sakurai},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2608.27570},
  eprint = {2608.27570},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.27570},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Elementary divisors of the Cartan matrix for partial characters
AU  - Kaveh Dastouri
AU  - Taro Sakurai
PY  - 2026
DA  - 2026/08/27
PB  - arXiv
DO  - 10.48550/arxiv.2608.27570
UR  - https://arxiv.org/abs/2608.27570
AB  - Let π be a set of primes and let G be a finite π-separable group. We prove that the Cartan matrix C for the π-partial characters of G is equivalent over the integers to a matrix diag(|C_G(x)|_π'), where x runs over a set of representatives of the π-classes of G. In particular, we prove that det C = ∏ |C_G(x)|_π'.
ER  -