# congruence lattice

## Which lattices occur as intervals in subgroup lattices of finite groups? ★★★★

Author(s):

\begin{conjecture} % Enter your conjecture in LaTeX % You may change "conjecture" to "question" or "problem" if you prefer. There exists a finite lattice that is not an interval in the subgroup lattice of a finite group. \end{conjecture}

Keywords: congruence lattice; finite groups

## Finite Lattice Representation Problem ★★★★

Author(s):

\begin{conjecture} % Enter your conjecture in LaTeX % You may change "conjecture" to "question" or "problem" if you prefer. There exists a finite lattice which is not the congruence lattice of a finite algebra. \end{conjecture}

Keywords: congruence lattice; finite algebra