## Details

Original language | English |
---|---|

Pages (from-to) | 4597-4614 |

Number of pages | 18 |

Journal | Proceedings of the American Mathematical Society |

Volume | 148 |

Issue number | 11 |

Publication status | Published - Nov 2020 |

## Abstract

Let p β₯ 5 be a prime and let G be a finite group. We prove that G is p-solvable of p-length at most 2 if there are at most two distinct p-character degrees in the principal p-block of G. This generalizes a theorem of Isaacs-Smith as well as a recent result of three of the present authors.

## Keywords

- P-character degrees, Principal block

## ASJC Scopus subject areas

**Mathematics(all)**- Mathematics(all)
**Applied Mathematics**

## Cite this

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**Groups with few πβ-character degrees in the principal block.**/ Giannelli, Eugenio; Rizo, Noelia; Sambale, Benjamin et al.

In: Proceedings of the American Mathematical Society, Vol. 148, No. 11, 11.2020, p. 4597-4614.

Research output: Contribution to journal βΊ Article βΊ Research βΊ peer review

*Proceedings of the American Mathematical Society*, vol. 148, no. 11, pp. 4597-4614. https://doi.org/10.1090/proc/15143

*Proceedings of the American Mathematical Society*,

*148*(11), 4597-4614. https://doi.org/10.1090/proc/15143

}

TY - JOUR

T1 - Groups with few νβ-character degrees in the principal block

AU - Giannelli, Eugenio

AU - Rizo, Noelia

AU - Sambale, Benjamin

AU - Schaeffer Fry, A. A.

N1 - Funding Information: Received by the editors September 18, 2019. 2010 Mathematics Subject Classification. Primary 20C15, 20C30, 20C33. Key words and phrases. pβ²-character degrees, principal block. The second author was partially supported by the Spanish Ministerio de Ciencia e InnovaciΓ³n PID2019-103854GB-I00 and FEDER funds. The third author was supported by the German Research Foundation (SA 2864/1-1 and SA 2864/3-1). The fourth author was partially supported by a grant from the National Science Foundation (Award No. DMS-1801156). Part of this work was completed while the second and fourth authors were in residence at the Mathematical Sciences Research Institute in Berkeley, CA, during Summer 2019 under grants from the National Security Agency (Award No. H98230-19-1-0119), The Lyda Hill Foundation, The McGovern Foundation, and Microsoft Research.

PY - 2020/11

Y1 - 2020/11

N2 - Let p β₯ 5 be a prime and let G be a finite group. We prove that G is p-solvable of p-length at most 2 if there are at most two distinct p-character degrees in the principal p-block of G. This generalizes a theorem of Isaacs-Smith as well as a recent result of three of the present authors.

AB - Let p β₯ 5 be a prime and let G be a finite group. We prove that G is p-solvable of p-length at most 2 if there are at most two distinct p-character degrees in the principal p-block of G. This generalizes a theorem of Isaacs-Smith as well as a recent result of three of the present authors.

KW - P-character degrees

KW - Principal block

UR - http://www.scopus.com/inward/record.url?scp=85092763352&partnerID=8YFLogxK

U2 - 10.1090/proc/15143

DO - 10.1090/proc/15143

M3 - Article

AN - SCOPUS:85092763352

VL - 148

SP - 4597

EP - 4614

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 11

ER -