Unsolved Problems

Problem Does there exist a finitely presented group of intermediate growth?...

Conjecture Suppose $G$ is a finite group, and $n$ is a positive integer dividing $|G|$. Suppose that $G$ has exactly $n$ solutions to $x^{n} = 1$. Do...

Conjecture If a group has $r$ generators and exponent $n$, is it necessarily finite?...

Conjecture Every finite group is the Galois group of some finite algebraic extension of $\mathbb Q$....

Conjecture There exists a finite lattice that is not an interval in the subgroup lattice of a finite group....