论文标题
线性代数群体中的换向器的能力
Powers of commutators in linear algebraic groups
论文作者
论文摘要
令$ {\ mathscr g} $为$ k $的线性代数群，其中$ k $是代数封闭的字段，伪限制字段或非Archimedean本地字段的估值环。令$ g = {\ mathscr g}（k）$。我们证明，如果$γ，δ\在g $中，则$γ$是换向器，而$ \langleΔ\ rangle = \langleγ\ rangle $，则$δ$是换向器。这概括了有限群体本田的结果。我们的证明使用了一阶模型理论的Lefschetz原理。
Let ${\mathscr G}$ be a linear algebraic group over $k$, where $k$ is an algebraically closed field, a pseudo-finite field or the valuation ring of a nonarchimedean local field. Let $G= {\mathscr G}(k)$. We prove that if $γ, δ\in G$ such that $γ$ is a commutator and $\langle δ\rangle= \langle γ\rangle$ then $δ$ is a commutator. This generalises a result of Honda for finite groups. Our proof uses the Lefschetz Principle from first-order model theory.
