Determination of conjugacy class sizes from products of characters

Groups Whose Nonlinear Irreducible Characters Separate Element Orders or Conjugacy Class Sizes

A class function φ on a finite group G is said to be an order separator if, for every x and y in G\{1} , φ(x) = φ(y) is equivalent to x and y being of the same order. Similarly, φ is said to be a class-size separator if, for every x and y in G \ {1} , φ(x) = φ(y) is equivalent to |CG(x)| = |CG(y)| . In this paper, finite groups whose nonlinear irreducible complex characters are all order separa...

p-divisibility of conjugacy class sizes and normal p-complements

LetN be a normal subgroup of a groupG and let p be a prime. We prove that if the p-part of jx j is a constant for every prime-power order element x 2 N n Z.N /, then N is solvable and has normal p-complement.

Fixed Point Spaces, Primitive Character Degrees and Conjugacy Class Sizes

Irreducible characters which are zero on only one conjugacy class

Suppose that G is a …nite solvable group which has an irreducible character which vanishes on exactly one conjugacy class. Then we show that G has a homomorphic image which is a nontrivial 2-transitive permutation group. The latter groups have been classi…ed by Huppert. We can also say more about the structure of G depending on whether is primitive or not. Mathematics Subject Classi…cation 2000...

Conjugacy Separability of a Class of 1-relator Products

We prove the conjugacy separability of groups of the form G = (ax,...ar,bx,...,bs:aeli = bf> = (U(ax, ... , ar)V{bx , ... , bs))m = 1), where m > 1 .