In this paper we measure how efficiently a finite simple group G is generated by its elements of order p, where p is a fixed prime. This measure, known as the p-width of G, is the minimal k ∈ ℕ such that any g ∈ G can be written as a product of at most k elements of order p. Using primarily character theoretic methods, we sharply bound the p-width of some low rank families of Lie type groups, as well as the simple alternating and sporadic groups.

中文翻译：

---

关于有限单群的 p 宽度

在本文中，我们测量了有限单群G由其p阶元素生成的效率，其中p是固定素数。这个度量，称为G的p宽度，是最小k ∈ ℕ 使得任何g ∈ G可以写成最多k 个p阶元素的乘积。主要使用特征理论方法，我们严格限制了一些 Lie 型群的低阶族以及简单的交替群和零星群的p宽度。