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Journal of Lie Theory 25 (2015), No. 3, 889--901
Copyright Heldermann Verlag 2015

On a Question of Ross and Stromberg

Hatem Hamrouni
Dept. of Mathematics, Faculty of Sciences at Sfax, Sfax University, B.P. 1171, 3000 Sfax, Tunisia

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.

Keywords: Locally compact group, Lie group, pro-Lie group, pro-torus, compact element, projective limit, Chabauty topology.

MSC: 22D05

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