On Andrews-Curtis conjectures for soluble groups

2016/12/20 by Guyot, Luc
#FOS: Mathematics #Group Theory (math.GR) #Primary 20F05 #Secondary 20F16

paper · doi:10.48550/arxiv.1612.06912

Abstract

The Andrews-Curtis conjecture claims that every normally generating n-tuple of a free group F_n of rank n ≥ 2 can be reduced to a basis by means of Nielsen transformations and arbitrary conjugations. Replacing F_n by an arbitrary finitely generated group yields natural generalizations whose study may help disprove the original and unsettled conjecture. We prove that every finitely generated soluble group satisfies the generalized Andrews-Curtis conjecture in the sense of Borovik, Lubotzky and Myasnikov. In contrast, we show that some soluble Baumslag-Solitar groups do not satisfy the generalized Andrews-Curtis conjecture in the sense of Burns and Macedońska.

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