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- W2624259589 abstract "We study the automorphism group of Hallâs universal locally finite group $H$. We show that in $Aut(H)$ every subgroup of index $< 2^{aleph _0}$ 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 the second author it follows that for every countable locally finite $G$ there exists $G cong Gâ leqslant H$ such that every $f in Aut(Gâ)$ extends to an $hat {f} in Aut(H)$ in such a way that $f mapsto hat {f}$ embeds $Aut(Gâ)$ into $Aut(H)$. In particular, we solve the three open questions of Hickin on $Aut(H)$ from his 1978 work, and give a partial answer to Question VI.5 of Kegel and Wehrfritz from their 1973 work." @default.
- W2624259589 created "2017-06-15" @default.
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- W2624259589 date "2017-11-07" @default.
- W2624259589 modified "2023-09-27" @default.
- W2624259589 title "The automorphism group of Hall’s universal group" @default.
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- W2624259589 doi "https://doi.org/10.1090/proc/13836" @default.
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