\(nX\)-complementary generations of the sporadic group \(Co_1\). (Q1884469)

A finite group \(G\) with a conjugacy class \(X\) is said to be \(X\)-complementary generated if, for every non-trivial \(x\in G\), there exists an element \(y\in X\) such that \(G=\langle x,y\rangle\). The authors prove that the simple sporadic group \(G=Co_1\) is \(X\)-complementary generated if and only if \(X\) consists of elements of order greater than 3 and \(X\not\in\{4A,4B,4C,4D,5A,6A\}\).