# Andrews-Curtis conjecture

From Groupprops

This article is about a conjecture in the following area in/related to group theory: free groups. View all conjectures and open problems

*This conjecture is believed to be false*

## Statement

Let denote the free group on elements with a set a freely generating set. Then, the following holds:

A set of elements of generates as a normal subgroup if and only if is Andrews-Curtis equivalent to , viz one can get from to by a sequence of Nielsen transformations along with inner automorphisms from .

There is also a stronger version, the stable Andrews-Curtis conjecture.