Remarks on some one-ended groups

Abstract In this note, we study the condition of being one-ended for a particular class of discrete groups, namely groups acting freely and co-compactly on some CAT(0) square complexes. In particular, we furnish an algorithm that associates to a one-ended squared group another square complex which is “smaller” and more tractable than the one given by the definition of the group, in particular with nicer local connectivity conditions.