On infinitely presented soluble groups

For groups with finitely many generators and relators, one can always obtain a minimal group presentation by deleting redundant relators. I will show that such a process does not apply to infinitely presented groups by exhibiting a finitely generated group with no minimal group presentations. The counterexample I will present is moreover 4-soluble and enjoys very special features within the space of marked groups. I will then investigate where soluble groups are located in the space of marked groups, depending on whether they are finitely presented or not. This is a joint work with Yves de Cornulier.