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maximal subgroup
Let be a group.
A subgroup of is said to be a maximal subgroup of if and there is no subgroup of such that . Note that a maximal subgroup of is not maximal among all subgroups of , but only among all proper subgroups of . For this reason, maximal subgroups are sometimes called maximal proper subgroups.
Similarly, a normal subgroup of is said to be a maximal normal subgroup (or maximal proper normal subgroup) of if and there is no normal subgroup of such that . We have the following theorem:
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new image: sinx_approx.png by jeremyboden
new image: approximation_to_sinx by jeremyboden
new image: approximation_to_sinx by jeremyboden
new question: Solving the word problem for isomorphic groups by mairiwalker
new image: LineDiagrams.jpg by m759
new image: ProjPoints.jpg by m759
new image: AbstrExample3.jpg by m759
new image: four-diamond_figure.jpg by m759
May 16
new problem: Curve fitting using the Exchange Algorithm. by jeremyboden
new question: Undirected graphs and their Chromatic Number by Serchinnho


