Thomas P. Wakefield

Verifying Huppert's Conjecture for PSL3(q) and PSU3(q 2)

Let G be a finite group and cd(G) be the set of irreducible character degrees of G. Bertram Huppert conjectured that if H is a finite nonabelian simple group such that cd(G) = cd(H), then G ≅ H × A, where A is an abelian group. We examine arguments to verify this conjecture for the simple groups of Lie type of rank two. To illustrate our arguments, we extend Hupperts results and verify the conjecture for the simple linear and unitary groups of rank two.

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

Let G denote a finite group and cd(G) the set of irreducible character degrees of G. Huppert conjectured that if H is a finite nonabelian simple group such that cd(G) = cd(H), then G ∼= H×A, where A is an abelian group. He verified the conjecture for many of the sporadic simple groups and we complete its verification for the remainder.

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

Let

Current state and potential of additive – hybrid manufacturing for metal parts

G

On Huppert's Conjecture for Alternating Groups of Low Degrees

be a finite group and let

On Huppert’s Conjecture for the Monster and Baby Monster

cd(G)

Verifying Huppert’s Conjecture for PSp 4 ( q ) when q > 7

be the set of all irreducible complex character degrees of

Verifying Huppert's Conjecture for 2 G 2 (q 2 )

G

On Huppert’s conjecture for G2(q), q≥7

. It was conjectured by Huppert in Illinois J. Math. 44 (2000) that, for every non-abelian finite simple group

On a group with three supersolvable subgroups of pairwise relatively prime indices

H