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By definition, a constructible totally disconnected, locally compact (tdlc) group is the result of a sequence of profinite extensions and ascending HNN-extensions starting from the trivial group. As in the discrete case, soluble constructible tdlc groups have type $FP_\infty$ (G. C. Cook, I. Castellano, J. Algebra, 543 (2020), 54–97). Are soluble tdlc groups of type $FP_\infty$ constructible?

Contributor: G. C. Cook

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