A characterization of the simple groups PSp(4, 3) and PSp(6, 2)

Finite groups with a certain centralizer of an element of order 3

“…These characterizations of S 9 are similar to the characterizations of PSp (4,3) and PSp (6,2) in [4] and [6]. The main theorem is used in the author's characterization of the simple group 2 D 4 (2) by its 3-centralizer structure [7].…”

“…In S 9 , let M = <(1,2,3), (4,5,6), (7,8,9)), x = (1, 4, 7) (2, 5, 8) (3, 6, 9), t = (1,4) (2, 5) (3,6), and let P = M(x). Then the centralizer C in S 9 of (1,2,3) (4, 5, 6) (7,8,9) is P(t).…”

A 3-local identification of two almost simple extensions of PΩ8+(2)

“…So w g lies in a K -orbit of length either 54 or 27. Hence |C T (w g )| 2 11 which implies that |C T (w g )| 2 11 . Therefore w g / ∈ E. So we have w g ∈ T ‡ \ E. Since |C T (w g )| = 2 10 , |C E (w g )| 2 6 .…”

A 3-local characterization of U6(2) and Fi22

“…We shall, in particular, exploit a theorem of Hayden [11] which identifies PSp 4 (3) by the centralizer of its non-trivial 3-central elements and a certain further 3-local condition. We mention that other contributions in this area include work by Higman [8], Hayden [12] and Prince [19][20][21]. These results form the foundation upon which we build our identifications.…”