Sh:1106
- Paolini, G., & Shelah, S. (2018). The automorphism group of Hall’s universal group. Proc. Amer. Math. Soc., 146(4), 1439–1445. arXiv: 1703.10540 DOI: 10.1090/proc/13836 MR: 3754331
-
Abstract:
We study the automorphism group of Hall’s universal locally finite group . We show that in every subgroup of index lies between the pointwise and the setwise stabilizer of a unique finite subgroup of , and use this to prove that is complete. We further show that is the largest locally finite normal subgroup of . Finally, we observe that from the work of [312] it follows that for every countable locally finite there exists such that every extends to an in such a way that embeds into . In particular, we solve the three open questions of Hickin on from [3] and give a partial answer to Question VI.5 of Kegel and Wehrfritz from [6]. - published version (7p)
Bib entry
@article{Sh:1106, author = {Paolini, Gianluca and Shelah, Saharon}, title = {{The automorphism group of Hall's universal group}}, journal = {Proc. Amer. Math. Soc.}, fjournal = {Proceedings of the American Mathematical Society}, volume = {146}, number = {4}, year = {2018}, pages = {1439--1445}, issn = {0002-9939}, mrnumber = {3754331}, mrclass = {20B27 (03C60 20F50)}, doi = {10.1090/proc/13836}, note = {\href{https://arxiv.org/abs/1703.10540}{arXiv: 1703.10540}}, arxiv_number = {1703.10540} }