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In mathematics, the lattice of subgroups of a group is the lattice whose elements are the subgroups of , with the partial order relation being set inclusion. In this lattice, the join of two subgroups is the subgroup generated by their union, and the meet of two subgroups is their intersection. == Example == The dihedral group Dih4 has ten subgroups, counting itself and the trivial subgroup. Five of the eight group elements generate subgroups of order two, and two others generate the same cyclic group Z4. In addition, there are two groups of the form Z2 × Z2, generated by pairs of order-two elements. The lattice formed by these ten subgroups is shown in the illustration. This example also shows that the lattice of all subgroups of a group is not a modular lattice in general. Indeed, this particular lattice contains the forbidden "pentagon" ''N''5 as a sublattice. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Lattice of subgroups」の詳細全文を読む スポンサード リンク
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