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This paper continues previous work, based on systematic use of a formula of L. Scott, to detect Hurwitz groups. It closes the problem of determining the finite simple groups contained in PGL n ( F ) for n ≤ 7 which are Hurwitz, where F is an algebraically closed field. For the groups G 2 ( q ) , q ≥ 5 , and the Janko groups J 1 and J 2 it provides explicit ( 2 , 3 , 7 ) -generators. [ABSTRACT FROM AUTHOR]

If G is a finite group and X a conjugacy class of elements of G, then we define rank(G : X) to be the minimum number of elements of X generating G. In the present paper we study the rank(Ji : X) for all conjugacy classes of Ji, where i = 1; 2; 3; 4. [ABSTRACT FROM AUTHOR]

A partition for the elements of prime-power order in a finite group G is a family of subgroups with the property that every non-identity element of prime-power order lies in exactly one subgroup of the family. The main result of this paper is a classification of the finite simple groups which have such a partition. We also establish a connection between this concept and the class of permutation groups all of whose elements of prime-power order have the same number of fixed points. [ABSTRACT FROM AUTHOR]