Groups St Andrews 2001 in Oxford 2003
DOI: 10.1017/cbo9780511542787.012
|View full text |Cite
|
Sign up to set email alerts
|

Characters of p-groups and Sylow p-subgroups

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
2
2

Citation Types

2
17
0

Year Published

2005
2005
2023
2023

Publication Types

Select...
6

Relationship

0
6

Authors

Journals

citations
Cited by 18 publications
(19 citation statements)
references
References 34 publications
2
17
0
Order By: Relevance
“…Let G be a finite group and Irr(G) the set of irreducible complex characters of G. Let ep(G) be the largest integer such that p ep(G) divides χ(1) for some χ ∈ Irr(G). We show that |G : F(G)|p ≤ p kep(G) for a constant k. This settles a conjecture of A. Moretó [17, Conjecture 4].…”
supporting
confidence: 79%
See 2 more Smart Citations
“…Let G be a finite group and Irr(G) the set of irreducible complex characters of G. Let ep(G) be the largest integer such that p ep(G) divides χ(1) for some χ ∈ Irr(G). We show that |G : F(G)|p ≤ p kep(G) for a constant k. This settles a conjecture of A. Moretó [17, Conjecture 4].…”
supporting
confidence: 79%
“…In this paper, we show that for arbitrary group, |G : F(G)| p ≤ p kep(G) for some constant k. This settles [17,Conjecture 4].…”
Section: Introductionsupporting
confidence: 58%
See 1 more Smart Citation
“…Let p a denote the largest power of p dividing χ(1) for an irreducible character χ of G and b(P ) denote the largest degree of an irreducible character of P . Conjecture 4 of Moretó [18] suggested log b(P ) is bounded as a function of a. Moretó and Wolf [20] have proven this for G solvable and even something a bit stronger, namely the logarithm to the base of p of the p-part of |G : F(G)| is bounded in terms of a. In fact, they showed that |G : F(G)| p ≤ p 19a .…”
Section: P Part Of |G : F(g)| and Irreducible Character Degreesmentioning
confidence: 96%
“…This bound is best possible, as shown by an example in [5]. It is possible that p a < b(P ) at least when p = 2, as shown by an example of Isaacs [18,Example 5.1].…”
Section: P Part Of |G : F(g)| and Irreducible Character Degreesmentioning
confidence: 99%