2 problems

Let $F_2$ be the free group on two generators, and let $A_n$ denote the alternating group on $n$ elements. A finite quotient of $F_2$ is characteristic when it is of the form…

Let $F_n$ denote the free group on $n$ generators. A subgroup $C\leq F_n$ is characteristic if it is preserved by every automorphism of $F_n$. The Baby Wiegold conjecture. For ever…