New posts in Free Groups

Normal generation of the kernel of a surjection of free groups

Can two elliptic isometries generate a free group?

Intuition of characteristic property of the free group

Let $G$ be a group with a free subgroup of rank $2$. Let $H\leq G$ be such that $[G:H]<\infty$. Then $H$ also contains a free subgroup of rank $2$.

One missing step in proving $\mathbb{Z}\times \mathbb{Z} \cong \langle a,b\,|\, [a,b]=1\rangle$

Motivation for definition of free group?

Question about $\operatorname{Aut}(D_\infty)\cong D_\infty$

Is the free group on two generators generated by two elements as a monoid?

Difference between "generating set" and free product?

Show that the free group on three generators is a subgroup of the free group on two generators