nLab
maximal subgroup

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Contents

Idea

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

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