A note on restriction of characters of alternating groups to Sylow subgroups

Giannelli, Eugenio

doi:10.1016/j.jalgebra.2018.11.026

Search citation statements

Order By: Relevance

Paper Sections

Select...

Introduction1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2020

2021

Publication Types

Select...

Article3

Other1

Relationship

Self Cite0

Independent4

Authors

Journals

Cited by 4 publications

(1 citation statement)

References 12 publications

(20 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In particular, all irreducible characters θ ∈ Irr(P ) appear as constituents of χ P with multiplicity at least θ(1) in this case. In [7,8,9], Giannelli and Navarro investigated a more general situation where χ(1) is divisible by p and χ P has at least one linear constituent λ ∈ Irr(P ). They conjectured (and proved in many cases) that χ P has at least p distinct linear constituents.…”

Section: Introductionmentioning

confidence: 99%

Restrictions of characters in p-solvable groups

Rossi¹,

Sambale²

2021

Preprint

View full text Add to dashboard Cite

Let G be a p-solvable group, P ≤ G a p-subgroup and χ ∈ Irr(G) such that χ(1) p ≥ |G : P | p . We prove that the restriction χ P is a sum of characters induced from subgroups Q ≤ P such that χ(1) p = |G : Q| p . This generalizes previous results by Giannelli-Navarro and Giannelli-Sambale on the number of linear constituents of χ P . We provide some evidence for the statement above being true for arbitrary groups. This can be seen as an extension of Brauer-Nesbitt's theorem on characters of p-defect zero. It also extends a conjecture of Wilde.

show abstract

Section: Introductionmentioning

confidence: 99%