On the characterization of some non-abelian simple groups with few codegrees

On the Characterization of Sporadic Simple Groups by Codegrees

“…and PSL (3,3) by [1,4,10]. The conjecture has also been verified for PSL (3, q) and PSU(3, q) in [17] and 2 G 2 (q) in [11].…”

Recognising Ree Groups Using the Codegree Set

“…In [1], the conjecture was proven for 2 B 2 (2 2 f +1 ), where f ≥ 1, PSL (3,4), Alt 7 and J 1 . The conjecture also holds in the cases where H is M 11 , M 12 , M 22 , M 23 or PSL (3,3) by [9]. For PSL (3, q) and PSU (3, q), the conjecture was confirmed in [16].…”

On the Characterization of Alternating Groups by Codegrees

“…Then G ∼ = H. This conjecture appears in the Kourovka Notebook of Unsolved Problems in Group Theory as question 20.79 [18]. It has been verified for PSL(2, q), PSL (3,4), Alt 7 , J 1 , 2 B 2 (2 2f +1 ) where f ≥ 1, M 11 , M 12 , M 22 , M 23 and PSL (3,3) by [1,3,13]. The conjecture has also been verified for PSL (3, q) and PSU (3, q) in [19] and 2 G 2 (q) in [14].…”

“…In this case, A 8 ∼ = GL(4, 2) and 26 divides|A 8 |. Now, cod(A 8 ) = {1, 2 6 •3 2 •5, 2 5 •3 2 •5, 2 4 •3 2 •7, 2 6 •3•5, 2 4 •3 2 •5, 2 6 •3 2 , 2 6 •7, 2 3 •3 2 •5, 3 2 •5•7, 2 5 •3 2 } from[13]. We will look at each possibility for m in turn.…”