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Let $p$ be a fixed prime number. The main purpose of this paper is tointroduce the notion of \textit{irreducible} $p$-local compact group, whichprovides a first reduction towards a classification of all $p$-local compactgroups. In order to test this idea, in this note we describe all $p$-localcompact groups of rank $1$ in terms of this notion.

Irreducible $p$-local compact groups I. The structure of $p$-local compact groups of rank $1$