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.

## References

See also

Last revised on April 1, 2019 at 11:42:42. See the history of this page for a list of all contributions to it.