Products of conjugacy classes in Chevalley groups. II: Covering and generation
[For part I see the preceding review Zbl 1007.20041.] Let \(G\) be a simple algebraic group over an algebraically closed field \(K\). Let \(C\) be a conjugacy class of \(G\). Define the covering number \(\text{cn}(G)\) and the generating number \(\overline{\text{gen}}(G)\) as follows: \[ \text{cn}(G)=\min\{m\mid C^m=G\}, \] \[ \overline{\text{gen}}(G)=\min\{m\mid\text{there are }g_i\in C\text{ such that }\overline{\langle g_1,\dots,g_m\rangle}=G\}. \] The authors investigate the relationship between generating numbers and covering numbers. They obtain results such as \[ {1\over 2}\text{cn}(G)\leq\overline{\text{gen}}(G)\leq\text{cn}(G)+1. \]
scientific article; zbMATH DE number 1799794