Title: The Automorphism Group of Hall's Universal Group,
Abstract: We study the automorphism group of Hall's universal locally finite group $H$.
We show that in $Aut(H)$ every subgroup of index $< 2^\omega$ lies between the
pointwise and the setwise stabilizer of a unique finite subgroup $A$ of $H$,
and use this to prove that $Aut(H)$ is complete. We further show that $Inn(H)$
is the largest locally finite normal subgroup of $Aut(H)$. Finally, we observe
that from the work of [Sh:312] it follows that for every countable locally
finite $G$ there exists $G \cong G' \leq H$ such that every $f \in Aut(G')$
extends to an $\hat{f} \in Aut(H)$ in such a way that $f \mapsto \hat{f}$
embeds $Aut(G')$ into $Aut(H)$. In particular, we solve the three open
questions of Hickin on $Aut(H)$ from [3], and give a partial answer to Question
VI.5 of Kegel and Wehrfritz from [6].