### Abstract

We show that if p is an odd prime and G is a finite group satisfying the condition that p^{2} divides the degree of no irreducible character of G, then /G: O_{p}(G)/_{p} ≤ p^{4}, where O_{p}(G) is the largest normal p-subgroup of G, and if P is a Sylow p-subgroup of G, then P″ is subnormal in G. Our investigations suggest that if p^{a} is the largest power of p dividing the degrees of irreducible characters of G, then /G: O_{p}(G)/_{p} is bounded by p^{f(a)}, where f (a) is a function in a and P^{(a+1)} is subnormal in G.

Original language | English (US) |
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Pages (from-to) | 483-497 |

Number of pages | 15 |

Journal | Journal of the London Mathematical Society |

Volume | 92 |

Issue number | 2 |

DOIs | |

State | Published - Nov 20 2014 |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Journal of the London Mathematical Society*,

*92*(2), 483-497. https://doi.org/10.1112/jlms/jdv035

**P-parts of character degrees.** / Lewis, Mark L.; Navarro, Gabriel; Tiep, Pham Huu; Tong-Viet, Hung P.

Research output: Contribution to journal › Article

*Journal of the London Mathematical Society*, vol. 92, no. 2, pp. 483-497. https://doi.org/10.1112/jlms/jdv035

}

TY - JOUR

T1 - P-parts of character degrees

AU - Lewis, Mark L.

AU - Navarro, Gabriel

AU - Tiep, Pham Huu

AU - Tong-Viet, Hung P.

PY - 2014/11/20

Y1 - 2014/11/20

N2 - We show that if p is an odd prime and G is a finite group satisfying the condition that p2 divides the degree of no irreducible character of G, then /G: Op(G)/p ≤ p4, where Op(G) is the largest normal p-subgroup of G, and if P is a Sylow p-subgroup of G, then P″ is subnormal in G. Our investigations suggest that if pa is the largest power of p dividing the degrees of irreducible characters of G, then /G: Op(G)/p is bounded by pf(a), where f (a) is a function in a and P(a+1) is subnormal in G.

AB - We show that if p is an odd prime and G is a finite group satisfying the condition that p2 divides the degree of no irreducible character of G, then /G: Op(G)/p ≤ p4, where Op(G) is the largest normal p-subgroup of G, and if P is a Sylow p-subgroup of G, then P″ is subnormal in G. Our investigations suggest that if pa is the largest power of p dividing the degrees of irreducible characters of G, then /G: Op(G)/p is bounded by pf(a), where f (a) is a function in a and P(a+1) is subnormal in G.

UR - http://www.scopus.com/inward/record.url?scp=84943391817&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84943391817&partnerID=8YFLogxK

U2 - 10.1112/jlms/jdv035

DO - 10.1112/jlms/jdv035

M3 - Article

AN - SCOPUS:84943391817

VL - 92

SP - 483

EP - 497

JO - Journal of the London Mathematical Society

JF - Journal of the London Mathematical Society

SN - 0024-6107

IS - 2

ER -