Hung P. Tong-Viet

Simple classical groups of Lie type are determined by their character degrees

Let G be a finite group. Denote by Irr(G) the set of all irreducible complex characters of G. Let cd(G) be the set of all irreducible complex character degrees of G forgetting multiplicities, that is, cd(G)={χ(1):χ∈Irr(G)} and let X1(G) be the set of all irreducible complex character degrees of G counting multiplicities. Let H be a finite nonabelian simple classical group. In this paper, we will show that if G is a finite group and X1(G)=X1(H) then G is isomorphic to H. In particular, this implies that the nonabelian simple classical groups of Lie type are uniquely determined by the structure of their complex group algebras.

Symmetric groups are determined by their character degrees

Abstract Let G be a finite group. Let X 1 ( G ) be the first column of the ordinary character table of G. In this paper, we will show that if X 1 ( G ) = X 1 ( S n ) , then G ≅ S n . As a consequence, we show that S n is uniquely determined by the structure of the complex group algebra C S n .

INFLUENCE OF STRONGLY CLOSED 2-SUBGROUPS ON THE STRUCTURE OF FINITE GROUPS

Let

Complex group algebras of the double covers of the symmetric and alternating groups

H\leq K

ON HUPPERT’S CONJECTURE FOR THE CONWAY AND FISCHER FAMILIES OF SPORADIC SIMPLE GROUPS

be subgroups of a group G. We say that H is strongly closed in K with respect to G if whenever

Groups whose prime graphs have no triangles

a^g \in K

P-parts of character degrees

where

The simple Ree groups F42(q2) are determined by the set of their character degrees

a \in H, g \in G,

PROJECTIVE SPECIAL LINEAR GROUPS PSL4(q) ARE DETERMINED BY THE SET OF THEIR CHARACTER DEGREES

then

Normal Restriction in Finite Groups

a^g \in H.