论文标题
到自由小组的扩展
Onto extensions of free groups
论文作者
论文摘要
子组的扩展$ h \ leqslant k \ leqslant f_a $的自由等级$ | a | a | = r \ geqslant 2 $在每个环境免费基础上$ a'$，Stallings Graph $γ_{a'}（k）$ a'$ a'$ $γ__}（a）$ugγ_}（代数扩展是在进行的，Miasnikov-Ventura-Weil猜想，并以负面解决，首先是Parzanchevski-Puder对等级$ r = 2 $的首先解决，最近由Kolodner和Kolodner for General Cark。在本说明中，我们研究了自由组之间这种新型扩展的特性（以及完全在变体中），并研究了它们相应的闭合操作员。有趣的是，对双重概念的自然尝试（进入扩展）变得微不足道，使得在这种情况下不可能进行高伊拉哈西型定理。
An extension of subgroups $H\leqslant K\leqslant F_A$ of the free group of rank $|A|=r\geqslant 2$ is called onto when, for every ambient free basis $A'$, the Stallings graph $Γ_{A'}(K)$ is a quotient of $Γ_{A'}(H)$. Algebraic extensions are onto and the converse implication was conjectured by Miasnikov-Ventura-Weil, and resolved in the negative, first by Parzanchevski-Puder for rank $r=2$, and recently by Kolodner for general rank. In this note we study properties of this new type of extension among free groups (as well as the fully onto variant), and investigate their corresponding closure operators. Interestingly, the natural attempt for a dual notion -- into extensions -- becomes trivial, making a Takahasi type theorem not possible in this setting.
