  The Andrews-Curtis conjecture asserts that, for a free group $F_n$ of rank
$n$ and a free basis $(x_1,...,x_n)$, any normally generating tuple
$(y_1,...,y_n)$ is Andrews-Curtis equivalent to $(x_1,...,x_n)$. This
equivalence corresponds to the actions of $\operatorname{Aut}F_n$ and of $F_n$
on normally generating $n$-tuples. The equivalence corresponding to the action
of $\operatorname{Aut}F_n$ on generating $n$-tuples is called Nielsen
equivalence. The conjecture for arbitrary finitely generated group has its own
importance to analyse potential counter-examples to the original conjecture. We
study the Andrews-Curtis and Nielsen equivalence in the class of finitely
generated groups for which every maximal subgroup is normal, including
nilpotent groups and Grigorchuk groups.
