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We prove that every finitely generated soluble group satisfies the generalized Andrews\u2013Curtis conjecture in the sense of Borovik, Lubotzky and Myasnikov. In contrast, we show that some soluble Baumslag\u2013Solitar groups do not satisfy the generalized Andrews\u2013Curtis conjecture in the sense of Burns and Macedo\u0144ska.<\/jats:p>","DOI":"10.1142\/s0218196718500054","type":"journal-article","created":{"date-parts":[[2017,12,6]],"date-time":"2017-12-06T04:16:50Z","timestamp":1512533810000},"page":"97-113","source":"Crossref","is-referenced-by-count":0,"title":["On Andrews\u2013Curtis conjectures for soluble groups"],"prefix":"10.1142","volume":"28","author":[{"given":"Luc","family":"Guyot","sequence":"first","affiliation":[{"name":"EPFL ENT CBS BBP\/HBP. Campus Biotech. 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