P-parts of character degrees

Mark L. Lewis; Gabriel Navarro; Pham Huu Tiep; Hung P. Tong-Viet

doi:10.1112/jlms/jdv035

P-parts of character degrees

Mark L. Lewis, Gabriel Navarro, Pham Huu Tiep, Hung P. Tong-Viet

Mathematics

Research output: Contribution to journal › Article › peer-review

17 Scopus citations

Abstract

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: O_p(G)/_p ≤ p⁴, 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)
Pages (from-to)	483-497
Number of pages	15
Journal	Journal of the London Mathematical Society
Volume	92
Issue number	2
DOIs	https://doi.org/10.1112/jlms/jdv035
State	Published - Nov 20 2014

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1112/jlms/jdv035

Cite this

@article{eb48992918a94829acae838cb75d1670,

title = "P-parts of character degrees",

abstract = "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.",

author = "Lewis, {Mark L.} and Gabriel Navarro and Tiep, {Pham Huu} and Tong-Viet, {Hung P.}",

note = "Publisher Copyright: {\textcopyright} 2015 London Mathematical Society.",

year = "2014",

month = nov,

day = "20",

doi = "10.1112/jlms/jdv035",

language = "English (US)",

volume = "92",

pages = "483--497",

journal = "Journal of the London Mathematical Society",

issn = "0024-6107",

publisher = "John Wiley and Sons Ltd",

number = "2",

}

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

SN - 0024-6107

VL - 92

SP - 483

EP - 497

JO - Journal of the London Mathematical Society

JF - Journal of the London Mathematical Society

IS - 2

ER -

P-parts of character degrees

Abstract

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this