OPG-702
Open
Growth of finitely presented groups
Problem Does there exist a finitely presented group of intermediate growth?...
L2
OPG-732
Open
Subgroup formed by elements of order dividing n
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...
L1
OPG-760
Open
Burnside problem
Conjecture If a group has $r$ generators and exponent $n$, is it necessarily finite?...
L3
OPG-3572
Open
Inverse Galois Problem
Conjecture Every finite group is the Galois group of some finite algebraic extension of $\mathbb Q$....
L3
OPG-37302
Open
Which lattices occur as intervals in subgroup lattices of finite groups?
Conjecture There exists a finite lattice that is not an interval in the subgroup lattice of a finite group....
L3