由两个素数阶元素不变生成的有限群的结构
The structure of finite groups invariably generated by two elements of prime order
AI总结：
本文研究由两个不同素数阶元素不变生成的有限群结构，以s=2、t=3为例证明几乎单群由2、3阶元素不变生成当且仅同构于PGL₂(3^(2ᵇ))（b≥1）。
AI中文摘要：
若对所有g,h∈G，均有G=⟨a^g,b^h⟩，则称群G由两个元素a和b不变生成。本文对由两个不同素数阶s和t的元素不变生成的有限群给出结构描述，并以s=2、t=3为例说明主要结果的应用，特别证明：一个几乎单群由2阶和3阶元素不变生成当且仅当它同构于PGL₂(3^(2ᵇ))（其中b≥1）。
英文摘要：
A group $G$ is invariably generated by two elements $a$ and $b$ if $G=\langle a^g,b^h\rangle $ for all $g,h\in G$. This paper provides a structural description of finite groups invariably generated by two elements of distinct prime orders $s$ and $t$. We illustrate the use of our main result in a case study with $s=2$ and $t=3$. In particular we prove that an almost simple group is invariably generated by an element of order $2$ and an element of order $3$ if and only if it is isomorphic to $\mathrm{PGL}_2(3^{2^b})$ for some $b \ge 1$.
