We consider G, a linear algebraic group defined over $\Bbbk $ , an algebraically closed field (ACF). By considering $\Bbbk $ as an embedded residue field of an algebraically closed valued field K, we can associate to it a compact G-space $S^\mu _G(\Bbbk )$ consisting of $\mu $ -types on G. We show that for each $p_\mu \in S^\mu _G(\Bbbk )$ , $\mathrm {Stab}^\mu (p)=\mathrm {Stab}\left (p_\mu \right )$ is a solvable infinite algebraic group when $p_\mu $ is centered at infinity and residually algebraic. Moreover, we give a description of the dimension of $\mathrm {Stab}\left (p_\mu \right )$ in terms of the dimension of p.

我们考虑G ，一个在 $\Bbbk $ 上定义的线性代数群，一个代数闭域 (ACF)。通过将 $\Bbbk$ 视为代数闭值域K的嵌入剩余域，我们可以将其关联到由G上的 $\mu$ 类型组成的紧致G空间 $S^\mu _G(\Bbbk )$ . 我们证明对于每个 $p_\mu \in S^\mu _G(\Bbbk )$ , $\mathrm {Stab}^\mu (p)=\mathrm {Stab}\left (p_\mu \right )$ 是一个可解的无限代数群，当 $p_\mu $ 以无穷大为中心并且是残差代数的。此外，我们根据p的维数来描述 $\mathrm {Stab}\left (p_\mu \right )$ 的维数。