Journal of Lie Theory

no. 3
On a Question of Ross and Stromberg
Journal of Lie Theory, Volume 25 (2015) no. 3, pp. 889-901
A topological group G is called an [AFG]-group if G contains an increasing sequence of finite subgroups having a dense union. In this paper it is proved that the identity component G0 of a locally compact [AFG]-group G is a pro-torus. This partially answers an old open question posed by K. A. Ross and K. Stromberg [Pacific J. Math. 20 (1967) 135--147]. Other results included in this paper give a necessary and sufficient condition for an almost connected Lie group to be an [AFG]-group.
DOI: 10.5802/jolt.865
Classification: 22D05
Keywords: Locally compact group, Lie group, pro-Lie group, pro-torus, compact element, projective limit, Chabauty topology 
@article{JOLT_2015_25_3_a12,
     author = {H. Hamrouni},
     title = {On a {Question} of {Ross} and {Stromberg}},
     journal = {Journal of Lie Theory},
     pages = {889--901},
     year = {2015},
     volume = {25},
     number = {3},
     doi = {10.5802/jolt.865},
     zbl = {1330.22007},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.865/}
}
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H. Hamrouni. On a Question of Ross and Stromberg. Journal of Lie Theory, Volume 25 (2015) no. 3, pp. 889-901. doi: 10.5802/jolt.865

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