Generating triples of involutions of large sporadic groups.

In each finite simple sporadic group, excepting the Baby Monster group B, the Monster group M, the McLaughlin group McL and Mathieu groups M[sub11], M[sub22], M[sub23], three generating involutions, two of which commute, are found. If G is one of the groups M[sub12], M[sub24], HS, J[sub1], J[sub2], J[sub3], then we give pairs of numbers p, q, p ≤ q, such that p = |ik|, q = |jk| for some involutions i, j, k with condition |ij| = 2 generating the group G. The triples of involutions mentioned above are found with the use of the system of computer algebra GAP. Recall that any two involutions of the triple of involutions generating either McL, ore M[sub11], or M[sub22], or M[sub23] do not commute. This research was supported by the Russian Foundation for Basic Research, grant 02-01-00078. [ABSTRACT FROM AUTHOR]