\(nX\)-complementary generations of the sporadic group \(O'N\). (Q1769485)

If \(G\) is a finite group and \(C\) is a conjugacy class of elements of \(G\), then \(G\) is said to be \(C\)-complementary generated if for every non-trivial element \(x\) of \(G\), there is an element \(y\in C\) such that \(G\) is generated by \(x\) and \(y\). Clearly a non-Abelian finite simple group cannot be \(C\)-complementary generated if \(C\) is a class of elements of order 1 or 2. In this paper it is shown that the sporadic simple group of O'Nan is \(C\)-complementary generated for every other conjugacy class \(C\).