nLab maximal subgroup




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.


See also

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