On (2, 3, t)-Generations for the Conway Group Co₂

Abstract

Problem statement: In this article we investigate all the (2, 3, t)-generations for the Conway’s second largest sporadic simple group Co₂, where t is an odd divisor of order of Co₂. Approach: An (l, m, n)-generated group G is a quotient group of the triangle group T (l, m, n) = (x, y, z|x¹ = y^m = zⁿ = xyz = 1). A group G is said to be (2, 3, t)-generated if it can be generated by two elements x and y such that o(x) = 2, o(y) = 3 and o (xy) = t. Computations are carried out with the aid of computer algebra system GAP-Groups, Algorithms and Programming. Results and Conclusion: The Conway group Co₂ is (2, 3, t)-generated for t an odd divisor of order of Co₂ except when t = 5, 7, 9.