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Let G be a finite group and X be a conjugacy class of G. The rank of X in G, denoted by rank(G : X), is defined to be the minimum number of elements of X generating G. We investigate the ranks of the alternating group A11. We use the structure constants method to determine the ranks of all the non-trivial classes of the group A11. [ABSTRACT FROM AUTHOR]

A finite group G is called (l,m, n)-generated, if it is a quotient group of the triangle group T (l,m, n) = . In [24], Moori posed the question of finding all the (p, q, r) triples, where p, q and r are prime numbers, such that a non-abelian finite simple group G is a (p, q, r)-generated. In this paper we will establish all the (p, q, r)-generations of the Mathieu group M22. GAP [16] and the Atlas of finite group representations [30] are used in our computations. [ABSTRACT FROM AUTHOR]

Let G be a finite group and X be a conjugacy class of G. The rank of X in G, denoted by rank(G : X), is defined to be the minimal number of elements of X generating G. In this paper we establish some general results on the ranks of certain conjugacy classes of elements for simple alternating group A n . We apply these general results together with the structure constants method to determine the ranks of all the non-trivial classes of A 8 and A 9 . [ABSTRACT FROM AUTHOR]