Minimal generating sets of maximal size in finite monolithic groups. (Q387610)

Let \(G\) be a finite group and \(X\) be a generating set for \(G\). Then \(X\) is called a minimal generating set for \(G\) if no proper subset of \(X\) generates \(G\). The largest size of a minimal generating set for \(X\) is denoted by \(m(G)\). The aim of the present paper is to give an estimate for \(m(G)-m(G/N)\), where \(G\) is a primitive monolithic group with the unique minimal normal subgroup \(N\).