论文标题
在具有固定点具有可计数恩格尔的固定点的自态群体上
On profinite groups with automorphisms whose fixed points have countable Engel sinks
论文作者
论文摘要
$ g $的元素$ g $的engel水槽是$ {\ mathscr e}（g）$，以便每$ x \ in g $ in G $中的每一个足够长的换向器$ [... [[x，g]，g]，g]，\ dots，g]，\ dots，g] $属于$ {\ mathscr e}（g）（g）$。 （因此，$ g $正是我们可以选择$ {\ mathscr e}（g）= \ {1 \} $。 a \ setMinus \ {1 \} $ centralizer $ c_g（a）$的每个元素具有可计数（或有限的）engel sink，然后$ g $具有有限的普通亚组$ n $，因此$ g/n $是本地nilpotent。
An Engel sink of an element $g$ of a group $G$ is a set ${\mathscr E}(g)$ such that for every $x\in G$ all sufficiently long commutators $[...[[x,g],g],\dots ,g]$ belong to ${\mathscr E}(g)$. (Thus, $g$ is an Engel element precisely when we can choose ${\mathscr E}(g)=\{ 1\}$.) It is proved that if a profinite group $G$ admits an elementary abelian group of automorphisms $A$ of coprime order $q^2$ for a prime $q$ such that for each $a\in A\setminus\{1\}$ every element of the centralizer $C_G(a)$ has a countable (or finite) Engel sink, then $G$ has a finite normal subgroup $N$ such that $G/N$ is locally nilpotent.
