A characterization of projective special unitary group U3(5) by nse

A new characterization of A_{11}

“…Then |P 7 | | 7 3 . Since n 7 = s (9,2,3,2), (7,3,3,2), (8,3,3,2), (6,4,3,2), (7,4,3,2), (4,5,3,2), (5,5,3,2), (3,6,3,2), (1,7,3,2), (2,7,3,2), (9, 7, 1, 1), (9, 5, 2, 1), (8, 6, 2, 1), (9, 6, 2, 1), (6, 7, 2, 1), (7, 7, 2, 1), (4, 7, 3, 1), (5,7,3,1), (5,6,6,3,1), (6,…”

“…Let Comparing the sizes of elements of same order but disregarding the actual orders of elements in T (G) of the Thompson's Problem, in other words, it remains only nse(G), whether can it characterize finite simple groups? Theorem 1.2 [6,19,22,12,7,8,11,9] Let G be a group and H be Some projective special linear groups, U 3 (5), U 3 (7) or L 5 (2). Then nse (G)…”

“…If G ∼ = A 11 , then from[1], nse(G)=nse(A 11 ). So we assume that nse(G)=nse(A 11 ).By(1), π(G) {2,3,5,7,11,13,17, 23, 29, 31, 37, 41, 89, 101, 457381, 498961, 2044351}. Since 18315 > 1 is the only odd number, then s 2 = 18315 and 2 ∈ π(G).…”

A Characterization of U4(2) by Nse

“…In fact, a finite nonabelian simple group H is called characterizable by nse, if every finite group G with nse(G) = nse(H) implies that G ∼ = H. In [7,8,9,10,12,13,24] it is proved that the alternating groups A n , where n ∈ {7, 8}, the symmetric groups S n where n ∈ {3, 4, 5, 6, 7}, M 12 , L 2 (27), L 2 (q) where q ∈ {16, 17, 19, 23}, L 2 (q) where q ∈ {7, 8, 11, 13}, L 2 (q) where q ∈ {17, 27, 29}, are uniquely determined by nse(G). Besides, in [1,14,15,16] it is proved that U 3 (4), L 3 (4), U 3 (5), L 3 (5), are uniquely determined by nse(G). Recently, in [3,6,18,19], it is proved that the simple groups In an effort to fill some of the empty ground about the characterization of simple groups by nse, in this paper we will prove the following main theorem.…”

A Characterization of Projective Special Unitary Group PSU(3,3) and Projective Special Linear Group PSL(3,3) by NSE

“…In [6][7][8][9][10][11][12], it is proved that the alternating groups A n , where n ∈ {7, 8}, the symmetric groups S n where n ∈ {3, 4, 5, 6, 7}, M 12 , L 2 (27), L 2 (q) where q ∈ {16, 17, 19, 23}, L 2 (q) where q ∈ {7, 8, 11, 13}, L 2 (q) where q ∈ {17, 27, 29}, are uniquely determined by nse(G). Besides, in [13][14][15][16], it is proved that…”