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PreprintCC BY 4.0arXiv

Finite groups with a unique real $2$-block

  • Yu Zeng
  • Fuming Jiang
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Abstract

Let p be a prime, and let B be a p-block of a finite group G. A p-block B is called \emph{real} if the set of irreducible ordinary characters contained in B is invariant under complex conjugation. Motivated by Harris' classification of the finite groups with a unique p-block for an arbitrary prime p, and by McHugh and Schaeffer Fry's classification of the finite quasi-simple groups with a unique real $2$-block, we classify, in this paper, all finite groups admitting exactly one real $2$-block.

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Cite

BibTeXRIS
BibTeX
@misc{zeng2026finite,
  title = {{Finite groups with a unique real $2$-block}},
  author = {Yu Zeng and Fuming Jiang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.20203},
  eprint = {2609.20203},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.20203},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Finite groups with a unique real $2$-block
AU  - Yu Zeng
AU  - Fuming Jiang
PY  - 2026
DA  - 2026/09/24
PB  - arXiv
DO  - 10.48550/arxiv.2609.20203
UR  - https://arxiv.org/abs/2609.20203
AB  - Let p be a prime, and let B be a p-block of a finite group G. A p-block B is called \emph{real} if the set of irreducible ordinary characters contained in B is invariant under complex conjugation. Motivated by Harris' classification of the finite groups with a unique p-block for an arbitrary prime p, and by McHugh and Schaeffer Fry's classification of the finite quasi-simple groups with a unique real $2$-block, we classify, in this paper, all finite groups admitting exactly one real $2$-block.
ER  -