What question did this study set out to answer?

To establish that the identity component of a locally compact AFG-group is a pro-torus and to provide conditions for almost connected Lie groups to be AFG-groups.

March 29, 2026Open Access

On a Question of Ross and Stromberg

Key Points

To establish that the identity component of a locally compact AFG-group is a pro-torus and to provide conditions for almost connected Lie groups to be AFG-groups.
Analyzed the structure of locally compact AFG-groups
Developed mathematical proofs regarding group components and properties
Investigated necessary conditions for Lie groups to be classified as AFG-groups
The identity component of a locally compact AFG-group is established as a pro-torus.
Necessary and sufficient conditions for an almost connected Lie group to be an AFG-group were identified.

Abstract

A topological group G is said an AFG -group if G contains an increasing sequence of finite subgroups having dense union.In this paper it is proved that the identity component G 0 of a locally compact AFG -group G is a pro-torus.This partially answers an old open question posed by Ross and Stromberg in 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.

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