On the Janko Group J_4 Generated by (2, 3, t) Generators

摘要

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 J_4 where t is any odd divisor of |J_4|. This extends earlier results of Ganief and Moori [J. Algebra 212 (1999), 305-322].