Search results for "Solvable group"

Zeros of Primitive Characters in Solvable Groups

1999

Vertices for characters of $p$-solvable groups

2002

Suppose that G is a finite p-solvable group. We associate to every irreducible complex character X ∈ Irr(G) of G a canonical pair (Q, δ), where Q is a p-subgroup of G and δ ∈ Irr(Q), uniquely determined by X up to G-conjugacy. This pair behaves as a Green vertex and partitions Irr(G) into families of characters. Using the pair (Q, δ), we give a canonical choice of a certain p-radical subgroup R of G and a character η ∈ Irr(R) associated to X which was predicted by some conjecture of G. R. Robinson.

VARIATIONS ON THOMPSON'S CHARACTER DEGREE THEOREM

2001

If P is a Sylow- p -subgroup of a finite p -solvable group G , we prove that G^\prime \cap \bf{N}_G(P) \subseteq {P} if and only if p divides the degree of every irreducible non-linear p -Brauer character of G. More generally if π is a set of primes containing p and G is π-separable, we give necessary and sufficient group theoretic conditions for the degree of every irreducible non-linear p -Brauer character to be divisible by some prime in π. This can also be applied to degrees of ordinary characters.

HEIGHTS OF CHARACTERS IN BLOCKS OF $p$-SOLVABLE GROUPS

2005

In this paper, it is proved that if $B$ is a Brauer $p$ -block of a $p$ -solvable group, for some odd prime $p$ , then the height of any ordinary character in $B$ is at most $2b$ , where $p^b$ is the largest degree of the irreducible characters of the defect group of $B$ . Some other results that relate the heights of characters with properties of the defect group are obtained.

Inequalities for character degrees of solvable groups

1986

A note on character degrees of solvable groups

1987

Prime Factors of Character Degrees of Solvable Groups

1987

Homogeneous products of characters

2004

I. M. Isaacs has conjectured (see \cite{isa00}) that if the product of two faithful irreducible characters of a solvable group is irreducible, then the group is cyclic. In this paper we prove a special case of the following conjecture, which generalizes Isaacs conjecture. Suppose that $G$ is solvable and that $\psi,\phi\in\Irr(G)$ are faithful. If $\psi \phi=m\chi$ where $m$ is a positive integer and $\chi \in \Irr(G)$ then $\psi$ and $\phi$ vanish on $G- Z(G)$. In particular we prove that the above conjecture holds for $p$-groups.

Correspondences Between 2-Brauer Characters of Solvable Groups

2010

Let G be a finite solvable group and let p be a prime. Let P ∈ Syl p (G) and N = N G (P). We prove that there exists a natural bijection between the 2-Brauer irreducible characters of p′-degree of G and those of N G (P).

A partition of characters associated to nilpotent subgroups

1999

IfG is a finite solvable group andH is a maximal nilpotent subgroup ofG containingF(G), we show that there is a canonical basisP(G|H) of the space of class functions onG vanishing off anyG-conjugate ofH which consists of characters. ViaP(G|H) it is possible to partition the irreducible characters ofG into “blocks”. These behave like Brauerp-blocks and a Fong theory for them can be developed.