Corrigendum to “Decomposing locally compact groups into simple pieces” [Math. Proc. Camb. Phil. Soc. 150 (1) (2011) 97-128]

Abstract

(personal communication) pointed out an error in Proposition 2·6 from our paper [1]; we thank him for his perspicacious remark, as well as for helpful comments on an earlier version of this correction. That error is corrected below; as we shall see, it only affects the statements of Theorem B and Proposition 2·6. An independent inaccurracy in [1, Theorem E(ii)], pointed out to us by Alain Valette (personal communication), is also rectified below. All other results of the original paper hold without change.We retain all the notation and conventions from [1]; moreover any numbered statement quoted here refers to the corresponding statement from loc. cit. The invalid claim is that the intersection N is trivial, in the last sentence of the proof of Proposition 2·6. That proposition must be replaced by the following: PROPOSITION 2·6 (corrected). Let G be a compactly generated totally disconnected locally compact group without non-trivial compact or discrete normal subgroup. Then: (i) every non-trivial closed normal subgroup contains a minimal one; (ii) the set M of non-trivial minimal closed normal subgroups need not be finite, but the subset M na of its non-abelian elements is finite; (iii) each abelian M ∈ M is topologically locally finite, hence contained in RadAssertions (i) and (iv) are stated and correctly proved in [1]. The erroneous assertion in loc. cit. is that the whole set M is finite. Indeed, a counter-example is provided by the group (Q p ) n