Modular subgroup

In mathematics, in the field of group theory, a modular subgroup is a subgroup that is a modular element in the lattice of subgroups, where the meet operation is defined by the intersection and the join operation is defined by the subgroup generated by the union of subgroups.

By the modular property of groups, every quasinormal subgroup (that is, a subgroup that permutes with all subgroups) is modular. In particular, every normal subgroup is modular.

References

• Schmidt, Roland (1994), Subgroup Lattices of Groups, De Gruyter expositions in mathematics, vol. 14, Walter de Gruyter, p. 43, ISBN 9783110112139.