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This example illustrates several basic options used individually.
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Compare the output of the DrawNormalSubgroupLattice command with that of the DrawSubgroupLattice command. The DrawSubgroupLattice command highlights normal subgroups by default, so the highlighted vertices there correspond to the full set of vertices in the normal subgroup lattice.
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You can also use Cayley table groups and (finite) finitely presented groups.
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| (2) |
In the following example, both the center and derived subgroup are highlighted using the default highlight color.
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Since both subgroups are highlighted using the same color, it is not immediately apparent which is the center and which is the derived subgroup. To fix this, use different colors for the two subgroups, as follows.
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You can specify that several subgroups be highlighted with one color, while others are highlighted using a different color.
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The following example shows both the lower and upper central series of a nilpotent group highlighted using different colors, with the lower central series highlighted in blue and the upper central series highlighted in red. Notice that subgroups appearing in both series are highlighted in purple, which is the result of blending red and blue together.
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This illustrates how the derived series of a nilpotent group (a -group, in this case) converges to the trivial subgroup more quickly that the lower central series. The lower central series is highlighted in blue, as indicated; because no color is specified, the derived series of the group is highlighted using the default highlight color.
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You can animate how a normal series progresses through the normal subgroup lattice as in the following example. (Set the frames per second to a value of or before running the resulting animation.)
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To simultaneously animate the upper and lower central series of a nilpotent group, use the fact that they have the same length, equal to the nilpotency class of the group, as illustrated below.
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| (4) |
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