Edith Adan-Bante

Products of characters and derived length

Let G be a finite solvable group and χ∈Irr(G) be a faithful character. We show that the derived length of G is bounded by a linear function of the number of distinct irreducible constituents of χχ. We also discuss other properties of the decomposition of χχ into its irreducible constituents.

Symmetric Groups and Conjugacy Classes

Abstract Let S n be the symmetric group of degree n where n > 5. Given any non-trivial , we prove that the product of the conjugacy classes and is never a conjugacy class. Furthermore, if n is odd and not a multiple of three, then is the union of at least three distinct conjugacy classes. We also describe the elements in the case when is the union of exactly two distinct conjugacy classes.

Products of characters and derived length. II

Abstract Let G be a finite solvable group and χ, ψ ∈ Irr(G) be complex characters of G. Let α be an irreducible constituent of the product χ ψ. We show that the derived length of Ker(α ) | Ker( χψ ) is bounded by a linear function on the number of distinct irreducible constituents of χψ.

INDUCTION OF CHARACTERS AND FINITE

Let

p

G

-GROUPS

be a finite

Products of characters and finite p-groups

p

Conjugacy classes and finite p-groups

-group, where

Homogeneous products of characters

p

Products of characters and finite p-groups II

is an odd prime number,