The (2,3)-generation of the finite unitary groups

Abstract

In this paper we prove that the unitary groups SUn(q 2 ) are (2, 3)generated for any prime power q and any integer n ≥ 8. By previous results this implies that, if n ≥ 3, the groups SUn(q 2 ) and PSUn(q 2 ) are (2, 3)-generated, except when (n, q)

THE $\boldsymbol {(2,3)}$ -GENERATION OF THE FINITE SIMPLE ODD-DIMENSIONAL ORTHOGONAL GROUPS

“…Furthermore, (xy) n−2 has order p when n ∈ {11, 17}. For n = 11, we get that the order of ζ is 6, 9 or 12, in contrast with (xy) 9 of odd order p. For n = 17, the order of ζ is 9, 12, 15 or 18. However, (xy) 9 I 17 and the other values are in contrast with (xy) 15 of odd order p. For n ∈ {9, 13}, we apply the previous argument to other elements h such that dim(V 1 (h)) = 1.…”

“…https://doi.org/10.1017/S1446788724000016 Published online by Cambridge University Press [9] The (2, 3)-generation of orthogonal groups 9…”

The (2,3)-generation of the finite 8-dimensional orthogonal groups

“…The problem of determining which are exactly the members of this list L requires a lot of detailed analysis, especially in small dimensions. Thanks to the efforts of many authors (see in particular [9,11,12] and the references within) it remains open only for the orthogonal groups.…”