On the ranks of HS and McL Faryad Ali ∗ and Mohamed Ali Faya Ibrahim † Department of Mathematics, Faculty of Science, King Khalid University P.O. Box 9004, Abha, Saudi Arabia Abstract If G is a finite group and X a conjugacy class of G, then we define rank(G : X ) to be the minimum number of elements of X generating G. In the present paper, we determine the ranks of the sporadic simple groups HS and McL. Most of the calculations were carried out using the computer algebra system GAP [13]. 1 Introduction and Preliminaries Let G be a finite group and X ⊆ G. We denote the minimum number of elements of X generating G by rank(G : X ). In the present paper we investigate rank(G : X ) where X is a conjugacy class of G and G is a sporadic simple group. Moori in [9], [10] and [11] proved that 5 ≤ rank(Fi 22 :2A) ≤ 6 and rank(Fi 22 : 2B)= rank(Fi 22 :2C ) = 3 where 2A,2B and 2C are the conjugacy classes of invo- lutions of the smallest Fischer group Fi 22 as represented in the ATLAS [1]. Hall and Soicher in [6] proved that rank(Fi 22 :2A) = 6. Moori in [12] determined the ranks of the J anko group J 1 , J 2 and J 3 . In the present paper, we determine the ranks of the two sporadic simple groups, namely Higman-Sims group HS and McLaughlin group McL. For basic properties of HS and McL, character tables of these groups and their maximal subgroups we use ATLAS [1] and GAP [13]. For detailed information about the computational * E-Mail: Fali@kku.edu.sa † E-Mail: mafibraheem@kku.edu.sa 1