Search results for "combinatoric"

A counterexample to Feit's Problem VIII on decomposition numbers

2016

We find a counterexample to Feit's Problem VIII on the bound of decomposition numbers. This also answers a question raised by T. Holm and W. Willems.

Induction and Character Correspondences in Groups of Odd Order

2002

Abstract Let P be a Sylow p -subgroup of G . By Irr p ′ ( G ), we denote the set of irreducible characters of G which have degree not divisible by p . When G is a solvable group of odd order, M. Isaacs constructed a natural one-to-one correspondence *:Irr p ′ ( G ) → Irr p ′ ( N G ( P )) which depends only on G and P . In this paper, we show that if ξ G  = χ ∈ Irr p ′ ( G ), then (ξ*) N G ( P )  = χ*.

p-Parts of character degrees and the index of the Fitting subgroup

2014

Abstract In a solvable group G, if p 2 does not divide χ ( 1 ) for all χ ∈ Irr ( G ) , then we prove that | G : F ( G ) | p ≤ p 2 . This bound is best possible.

Prime divisors of character degrees

2008

Character restrictions and multiplicities in symmetric groups

2017

Abstract We give natural correspondences of odd-degree characters of the symmetric groups and some of their subgroups, which can be described easily by restriction of characters, degrees and multiplicities.

Groups with a small average number of zeros in the character table

2021

Abstract We classify finite groups with a small average number of zeros in the character table.

On the number of zeros in the columns of the character table of a group

2004

Generalized Braid Groups and Mapping Class Gropus

1997

Given a chord system of D2, we associate a generalized braid group, a surface and a homomorphism from this braid group to the mapping class group of the surface. We disprove a conjecture stated in an article by Perron and Vannier by showing that generally this homomorphism is not injective.

Some remarks on the Erdős-Turán conjecture

1993

THE ZONE MODULUS OF A LINK

2005

In this paper, we construct a conformally invariant functional for two-component links called the zone modulus of the link. Its main property is to give a sufficient condition for a link to be split. The zone modulus is a positive number, and its lower bound is 1. To construct a link with modulus arbitrarily close to 1, it is sufficient to consider two small disjoint spheres each one far from the other and then to construct a link by taking a circle enclosed in each sphere. Such a link is a split link. The situation is different when the link is non-split: we will prove that the modulus of a non-split link is greater than [Formula: see text]. This value of the modulus is realized by a spec…