Contents

group theory

# Contents

## Idea

A maximal subgroup of a given group $G$ is a subgroup which is not all of $G$ and not contained in any other subgroup of $G$.

Hence a maximal subgroup is a maximal element of the lattice of subgroups after removing the trivial subgroup $G \subset G$ itself. More concisely it is a coatom of $G$‘s subgroup lattice.