<i>p</i>-parts of character degrees

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

doi:10.1112/jlms/jdv035

Cited by 18 publications

(29 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The dual of the Ito-Michler theorem on the set of conjugacy class sizes is that every conjugacy class of G has p -size if and only if a Sylow p-subgroup of G is central. In this paper, we study the dual versions of the results of Lewis et al on the set of conjugacy class sizes and show that analogues of the main results of [3] and [2] hold.…”

Section: Introductionmentioning

confidence: 83%

“…In particular, this implies that |G : F(G)| p = 1, where F(G) is the Fitting subgroup of G. A natural generalisation of the Ito-Michler theorem is the following result of Lewis et al [3]: if G is solvable and e p (G) = 1, then |G : F(G)| p ≤ p 2 . In [2], Lewis et al studied a similar problem for arbitrary finite groups and showed that if G is finite and e p (G) = 1, then |G :…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

On -Parts of Conjugacy Class Sizes of Finite groups

Yang¹,

Qian

2018

Bull. Aust. Math. Soc.

View full text Add to dashboard Cite

Let $G$ be a finite group. Let $\operatorname{cl}(G)$ be the set of conjugacy classes of $G$ and let $\operatorname{ecl}_{p}(G)$ be the largest integer such that $p^{\operatorname{ecl}_{p}(G)}$ divides $|C|$ for some $C\in \operatorname{cl}(G)$. We prove the following results. If $\operatorname{ecl}_{p}(G)=1$, then $|G:F(G)|_{p}\leq p^{4}$ if $p\geq 3$. Moreover, if $G$ is solvable, then $|G:F(G)|_{p}\leq p^{2}$.

show abstract

Section: Introductionmentioning

confidence: 83%

Section: Introductionmentioning

confidence: 99%

On -Parts of Conjugacy Class Sizes of Finite groups

Yang¹,

Qian

2018

Bull. Aust. Math. Soc.

View full text Add to dashboard Cite

show abstract

“…Clearly

P ≲ Out (S)

. Since

S

is a

p^{'}

‐group, we know (see for example [, Lemma 2.3]) that

P S / S

is a normal cyclic subgroup of

G / S

. Let

P_{1}

be a subgroup of

P

of order

p

.…”

Section: Proposition Bmentioning

confidence: 99%

“…The results in the next lemma are due to Gagola (see or ). Lemma Let

S

be a nonabelian simple group and let

G

be an almost simple group with

S ⩽ G ⩽ Aut (S)

.…”

Section: Proposition Amentioning

confidence: 99%

See 1 more Smart Citation

A note on p-parts of character degrees

Qian

2018

Bull. London Math. Soc.

View full text Add to dashboard Cite

show abstract

The Fitting subgroup, p‐length, derived length and character table

Ahanjideh

2020

Mathematische Nachrichten

View full text Add to dashboard Cite

For a character χ of a finite group G, the number χcfalse(1false)=[G:kerχ]χ(1) is called the codegree of χ. Let N be a normal subgroup of G and set Irr(G|N)=Irr(G)−Irr(G/N).Let p be a prime. In this paper, we first show that if for two distinct prime divisors p and q of |N|, pq divides none of the codegrees of elements of Irr(G|N), then Fit(N)≠{1} and N is either p‐solvable or q‐solvable. Next, we classify the finite groups with exactly one irreducible character of the codegree divisible by p and, also finite groups whose codegrees of irreducible characters which are divisible by p are equal. Then, we prove that p‐length of a finite p‐solvable group is not greater than the number of the distinct codegrees of its irreducible characters which are divisible by p. Finally, we consider the case when the codegree of every element of Irr(G|N) is square‐free.

show abstract

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 p 2 divides the degree of no irreducible character of G,

Cited by 18 publications

References 21 publications

On -Parts of Conjugacy Class Sizes of Finite groups

On -Parts of Conjugacy Class Sizes of Finite groups

A note on p-parts of character degrees

The Fitting subgroup, p‐length, derived length and character table

Contact Info

Product

Resources

About