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No abstract

No abstract

Let Fq be a finite field of characteristic r and order q=ra, V=Fqn the vector space of finite dimension n⩾1 over Fq, and Mat (n, q) the matrix algebra on V. We denote by Hn(q) (or Hn if q is clear from the context) one of the following classical groups: Sp (n, q) (with n even), the symplectic group on V; O(n, q) (with q odd), one of the full orthogonal groups on V in odd characteristic; U(n, q) (with q a square), the full unitary group on V.

In this paper we determine the irreducible projective representations of sporadic simple groups over an arbitrary algebraically closed field F , whose image contains an almost cyclic matrix of prime-power order. A matrix M is called cyclic if its characteristic and minimum polynomials coincide, and we call M almost cyclic if, for a suitable α ∈ F , M is similar to diag(α · Id h , M1), where M1 is cyclic and 0 ≤ h ≤ n. The paper also contains results on the generation of sporadic simple groups by minimal sets of conjugate elements.