Aglaia Myropolska

The Andrews-Curtis conjecture asserts that for a free group Fn of rank n and a free basis (x_1,…,x_n), any normally generating tuple (y_1,…,y_n) is Andrews-Curtis equivalent to (x_1,…,x_n). The equivalence corresponds to the actions of AutFn and of Fn on normally generating tuples. The conjecture also makes sense for arbitrary finitely generated groups. Moreover, it is relevant to analysis of potential counter-examples to the original conjecture.
In the talk, we will give an introduction to the subject and then discuss the Andrews-Curtis equivalence in the class of finitely generated groups for which every maximal subgroup is normal, including nilpotent groups and Grigorchuk groups.