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updated link to Gap.app; remarked that xgap is included with GAP
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Russ Woodroofe
Russ Woodroofe
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  • Although you say you'd prefer not to use GAP, producing a Hasse diagram is very easy in GAP, at least with the right packages.
    You'll need the xgap GAP package; and either the xgap binaries, which requires an X Windows system (easiest done with Linux or a similar Unix-like system), or else Gap.app, which requires a Mac.
    Once you have these installed, start xgap/Gap.app, and follow these steps:
    • Type "GraphicSubgroupLattice(SymmetricGroup(4));"
    • In the window that pops up, go to the Subgroups | All Subgroups menu.

    The Hasse diagram of the subgroup lattice will appear.

  • It's also quite easy to show parts of the subgroup lattice -- essentially, you can take any list of subgroups and show the inclusion relations. To do this:
    • Type "GraphicSubgroupLattice(G);" as before.
    • Compute the list of subgroups you want to display. It should be the output of the last GAP command.
    • Go to the Subgroups | Insert Vertices menu.
    The Hasse diagram of the subposet consisting of subgroups from your list will appear.

    There's probably a comparably easy way to show Hasse diagrams in MAGMA. (But I'm telling you what I know...)

    Xgap is usually included with GAP, and is also available from:
    http://www.gap-system.org/Packages/xgap.html
    Gap.app is available from:
    http://cocoagap.sourceforge.net/https://cocoagap.sourceforge.io/

  • Although you say you'd prefer not to use GAP, producing a Hasse diagram is very easy in GAP, at least with the right packages.
    You'll need the xgap GAP package; and either the xgap binaries, which requires an X Windows system (easiest done with Linux or a similar Unix-like system), or else Gap.app, which requires a Mac.
    Once you have these installed, start xgap/Gap.app, and follow these steps:
    • Type "GraphicSubgroupLattice(SymmetricGroup(4));"
    • In the window that pops up, go to the Subgroups | All Subgroups menu.

    The Hasse diagram of the subgroup lattice will appear.

  • It's also quite easy to show parts of the subgroup lattice -- essentially, you can take any list of subgroups and show the inclusion relations. To do this:
    • Type "GraphicSubgroupLattice(G);" as before.
    • Compute the list of subgroups you want to display. It should be the output of the last GAP command.
    • Go to the Subgroups | Insert Vertices menu.
    The Hasse diagram of the subposet consisting of subgroups from your list will appear.

    There's probably a comparably easy way to show Hasse diagrams in MAGMA. (But I'm telling you what I know...)

    Xgap is available from:
    http://www.gap-system.org/Packages/xgap.html
    Gap.app is available from:
    http://cocoagap.sourceforge.net/

  • Although you say you'd prefer not to use GAP, producing a Hasse diagram is very easy in GAP, at least with the right packages.
    You'll need the xgap GAP package; and either the xgap binaries, which requires an X Windows system (easiest done with Linux or a similar Unix-like system), or else Gap.app, which requires a Mac.
    Once you have these installed, start xgap/Gap.app, and follow these steps:
    • Type "GraphicSubgroupLattice(SymmetricGroup(4));"
    • In the window that pops up, go to the Subgroups | All Subgroups menu.

    The Hasse diagram of the subgroup lattice will appear.

  • It's also quite easy to show parts of the subgroup lattice -- essentially, you can take any list of subgroups and show the inclusion relations. To do this:
    • Type "GraphicSubgroupLattice(G);" as before.
    • Compute the list of subgroups you want to display. It should be the output of the last GAP command.
    • Go to the Subgroups | Insert Vertices menu.
    The Hasse diagram of the subposet consisting of subgroups from your list will appear.

    There's probably a comparably easy way to show Hasse diagrams in MAGMA. (But I'm telling you what I know...)

    Xgap is usually included with GAP, and is also available from:
    http://www.gap-system.org/Packages/xgap.html
    Gap.app is available from:
    https://cocoagap.sourceforge.io/

    • Source Link
    Russ Woodroofe
    Russ Woodroofe
    • 3.4k
    • 1
    • 24
    • 22

  • Although you say you'd prefer not to use GAP, producing a Hasse diagram is very easy in GAP, at least with the right packages.
    You'll need the xgap GAP package; and either the xgap binaries, which requires an X Windows system (easiest done with Linux or a similar Unix-like system), or else Gap.app, which requires a Mac.
    Once you have these installed, start xgap/Gap.app, and follow these steps:
    • Type "GraphicSubgroupLattice(SymmetricGroup(4));"
    • In the window that pops up, go to the Subgroups | All Subgroups menu.

    The Hasse diagram of the subgroup lattice will appear.

  • It's also quite easy to show parts of the subgroup lattice -- essentially, you can take any list of subgroups and show the inclusion relations. To do this:
    • Type "GraphicSubgroupLattice(G);" as before.
    • Compute the list of subgroups you want to display. It should be the output of the last GAP command.
    • Go to the Subgroups | Insert Vertices menu.
    The Hasse diagram of the subposet consisting of subgroups from your list will appear.

    There's probably a comparably easy way to show Hasse diagrams in MAGMA. (But I'm telling you what I know...)

    Xgap is available from:
    http://www.gap-system.org/Packages/xgap.html
    Gap.app is available from:
    http://cocoagap.sourceforge.net/