On Thompson’s conjecture for finite simple groups

Abstract

Let G be a finite group, N(G) be the set of conjugacy classes of the group G. In the present paper it is proved G ≃ L if N(G) = N(L), where G is a finite group with trivial center and L is a finite simple group.

A note on the recognition of PSL2(p)

“…There has been significant progress in the study of this conjecture [2][3][4]. Especially, Gorshkov [4] claimed that he had proved Thompson's conjecture.…”

“…There has been significant progress in the study of this conjecture [2][3][4]. Especially, Gorshkov [4] claimed that he had proved Thompson's conjecture. Therefore, it is natural to investigate some problems beyond this conjecture.…”

On recognition of $A_6\times A_6$ by the set of conjugacy class sizes

“…In a series of papers of different authors, it took more than twenty years to confirm the conjecture. The final step was done in [4], where a full historical overview of the proof can be found.…”

Re-characterization of PGL(2, p) by its order and one class length

“…Then G is isomorphic to L if N (G) = N (L), where L is a nonabelian simple group. Recently, this conjecture was proved completely for all finite non-abelian simple group [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. Now, many mathematicians begin to study the extensive problems of the conjecture in different ways.…”