# Modular subgroup

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{{one source |date=April 2024}}
In [mathematics](/source/mathematics), in the field of [group theory](/source/group_theory), a '''modular subgroup''' is a [subgroup](/source/subgroup) that is a [modular element](/source/modular_lattice) in the [lattice of subgroups](/source/lattice_of_subgroups), where the meet operation is defined by the intersection and the join operation is defined  by the subgroup [generated](/source/generating_set_of_a_group) by the union of subgroups.

By the '''modular property of groups''', every [quasinormal subgroup](/source/quasinormal_subgroup) (that is, a subgroup that permutes with all subgroups) is modular. In particular, every [normal subgroup](/source/normal_subgroup) is modular.

==References==
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*{{citation|title=Subgroup Lattices of Groups|volume=14|series=De Gruyter expositions in mathematics|first=Roland|last=Schmidt|publisher=Walter de Gruyter|year=1994|isbn=9783110112139|page=43|url=https://books.google.com/books?id=EuVadOnix5MC&pg=PA43}}.
{{refend}}

Category:Subgroup properties

{{Group-theory-stub}}

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