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In this paper we determine the irreducible projective representations ofsporadic simple groups over an arbitrary algebraically closed field F, whoseimage contains an almost cyclic matrix of prime-power order. A matrix M iscalled cyclic if its characteristic and minimum polynomials coincide, and wecall M almost cyclic if, for a suitable a in F, M is similar to diag(a Id_h,M_1), where M_1 is cyclic and 0 <= h <= n. The paper also contains results onthe generation of sporadic simple groups by minimal sets of conjugate elements.

On generators and representations of the sporadic simple groups