交错群与嵌入由两个素数阶元素不变生成的群
Alternating Groups and Embeddings into Groups Invariably Generated by Two Prime-Order Elements
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中文总结 AI 辅助
该研究针对不同素数p、q，证明存在有限群无法嵌入由p阶与q阶元素不变生成的有限群，否定了《Kourovka Notebook》的相关问题，且当n足够大时交错群Aₙ无法嵌入这类群。
中文摘要 AI 辅助
对于任意不同素数p和q，我们证明存在一个有限群，它不能嵌入到任何由一个p阶元素和一个q阶元素不变生成的有限群中。这给出了对《Kourovka Notebook》第21.142号问题的否定回答。事实上，对于每一对固定的p、q，当n关于p和q足够大时，交错群Aₙ无法嵌入到这样的群中。
英文摘要
For any distinct primes $p$ and $q$, we prove that there is a finite group which does not embed into any finite group invariably generated by an element of order $p$ and an element of order $q$. This gives a negative answer to Problem 21.142 of the Kourovka Notebook \cite{kourovka21}. In fact, for every fixed pair $p,q$, the group $A_n$ cannot embed into such a group once $n$ is sufficiently large in terms of $p$ and $q$.
