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A group G is called (2, 3, t)-generated if it can be generated by two elements x and y in G such that o(x) = 2, o(y) = 3 and their product xy has order t. In the present article we investigate all (2, 3, t)-generations for the Janko's largest sporadic simple group J4 where t is any odd divisor of |J4|. This extends earlier results of Ganief and Moori [J. Algebra 212 (1999), 305-322]. [ABSTRACT FROM AUTHOR]

It is well known that all sporadic simple groups are (2,3,t)-generated, with the exception of M11, M22, M23 and McL. A group G is said to be (2,3,t)-generated if it can be generated by an involution x and an element y of order 3 such that o(xy) = t. In the present article, we investigate all (2,3,t)-generations for the Conway's first sporadic simple group Co1, where t is any odd divisor of |Co1|. Computations are carried out with the aid of computer algebra system GAP-Groups, Algorithms and Programming. [ABSTRACT FROM AUTHOR]

It is well known that all sporadic simple groups are (2,3,t)-generated, with the exception of M11, M22, M23 and McL. A group G is said to be (2,3,t)-generated if it can be generated by an involution x and an element y of order 3 such that o(xy) = t. In the present article, we investigate all (2,3,t)-generations for the Conway's first sporadic simple group Co1, where t is any odd divisor of |Co1|. Computations are carried out with the aid of computer algebra system GAP-Groups, Algorithms and Programming. [ABSTRACT FROM AUTHOR]