Covering numbers for Chevalley groups
Let \(G\) be a group. For a subset \(X\) of \(G\), let \(X^n\) denote the set of elements \(x_1\cdots x_n\), where \(x_i\in X\). If \(\mathfrak A\) is a set of subsets of \(G\), it is interesting to consider the problem to determine the smallest integer \(n\) such that \(X^n=G\) for all \(X\in{\mathfrak A}\). This is called the covering number, denoted by \(\text{cn}(G)\). The authors prove that, if \(G\) is a quasisimple Chevalley group with rank \(r\) and \(\mathfrak A\) is the set of non-central conjugacy classes, then there is a constant \(d\) such that \(\text{cn}(G)\leq dr\).
scientific article; zbMATH DE number 1356483
scientific article