AI 中文总结
本文证明Thompson群T的有限生成且不含任意高阶阿贝尔群的子群为虚阿贝尔或虚自由，进而得出曲面群不能嵌入T，解答了Belk与Moore的公开问题。
AI 中文摘要
确定曲面群能否嵌入Thompson群V是一个公开问题。本文证明，Thompson群T的任意有限生成、不含任意高阶阿贝尔群的子群，要么是虚阿贝尔的，要么是虚自由的。特别地，曲面群不能嵌入T，回答了Belk与Moore提出的问题。
英文摘要
It is an open problem to determine whether surface groups can embed in Thompson's group $V$. We prove that any finitely generated subgroup of Thompson's group $T$ without abelian groups of arbitrary high rank is either virtually abelian or virtually free. In particular, surface groups don't embed in $T$, answering a question of Belk and Moore.
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