Blocks of small defect

Yang, Yong

doi:10.1016/j.jalgebra.2014.10.048

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Cited by 16 publications

(13 citation statements)

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“…For a fixed prime

p

, the fundamental Ito–Michler theorem asserts that

p

does not divide

χ (1)

for any

χ \in Irr (G)

if and only if

G

has a normal abelian Sylow

p

‐subgroup. This result has been generalized in . In particular, the authors in studied the finite groups

G

in which

p^{2} d o e s n o t d i v i d e a n y i r r e d u c i b l e c h a r a c t e r d e g r e e .

For arbitrary groups

G

, it is shown that

false| G / O_{p} {false(G false) |}_{p}

is bounded by

p^{4}

when

p ⩾ 3

(see ), and by

p^{3}

when

p = 2

(see ).…”

Section: Introductionmentioning

confidence: 92%

A note on p-parts of character degrees

Qian

2018

Bull. London Math. Soc.

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“…For a fixed prime

p

, the fundamental Ito–Michler theorem asserts that

p

does not divide

χ (1)

for any

χ \in Irr (G)

if and only if

G

has a normal abelian Sylow

p

‐subgroup. This result has been generalized in . In particular, the authors in studied the finite groups

G

in which

p^{2} d o e s n o t d i v i d e a n y i r r e d u c i b l e c h a r a c t e r d e g r e e .

For arbitrary groups

G

, it is shown that

false| G / O_{p} {false(G false) |}_{p}

is bounded by

p^{4}

when

p ⩾ 3

(see ), and by

p^{3}

when

p = 2

(see ).…”

Section: Introductionmentioning

confidence: 92%

A note on p-parts of character degrees

Qian

2018

Bull. London Math. Soc.

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show abstract

“…Not much has been done on this problem. In a recent paper [24,Theorem B], the author obtained a partial result toward the previous question by showing the following. Let G be a finite solvable group, let p be a prime such that p ≥ 5 and O p (G) = 1, and we denote |G| p = p n .…”

Section: Introductionmentioning

confidence: 96%