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# 5.9 GraphicSubgroupLattice, Subgroups Menu

The `Subgroups` menu will be pulled down if you place the pointer inside the `Subgroups` button and press the left mouse button. Keep the button down and choose an entry by moving the pointer on top of this entry. Release the mouse button to select an entry.

Note that you can also get the `Subgroups` menu as a popup menu by clicking with the right mouse button into the graphic sheet of the subgroup lattice, but not on a vertex.

The result of a computation from any of the following entries is colored green, if your screen supports color. There will also be a short information message in the GAP window about the result.

In the following descriptions we use ``vertices'' as abbreviation for ``subgroups associated with vertices''.

The following descriptions do not apply to the case of finitely presented groups. See GraphicSubgroupLattice for FpGroups, Subgroups Menu for this case.

- `All Subgroups`

  For each selected vertex `All Subgroups` computes and displays all its subgroups. Requires at least one selected vertex. Use with care! This can cause huge computations! See also LatticeSubgroups in the GAP reference manual.

- `Centralizers`

  For each selected vertex `Centralizers` computes and displays its centralizer with respect to the whole group. Requires at least one selected vertex. See also Centralizer in the GAP reference manual.

- `Centres`

  For each selected vertex `Centres` computes and displays its centre. Requires at least one selected vertex. See also Centre in the GAP reference manual.

- `Closure`

  computes and displays the common closure of the selected vertices. Requires at least one selected vertex. See also ClosureGroup in the GAP reference manual.

- `Closures`

  computes and displays the closure of each pair of selected vertices. Requires at least two selected vertices. See also ClosureGroup in the GAP reference manual.

- `Commutator Subgroups`

  computes and displays the commutator subgroup of each pair of selected vertices. Requires at least two selected vertices. See also CommutatorSubgroup in the GAP reference manual.

- `Conjugate Subgroups`

  computes and displays the conjugacy class (with respect to the whole group) of each selected vertex. Requires at least one selected vertex. See also ConjugacyClass in the GAP reference manual.

- `Cores`

  For each selected vertex `Cores` computes and displays its core with respect to the whole group. Requires at least one selected vertex. See also Core in the GAP reference manual.

- `Derived Series`

  For each selected vertex `Derived Series` computes and displays its derived series. Requires at least one selected vertex. See also DerivedSeriesOfGroup in the GAP reference manual.

- `Derived Subgroups`

  For each selected vertex `Derived Subgroups` computes and displays its derived subgroup. Requires at least one selected vertex. See also DerivedSubgroup in the GAP reference manual.

- `Fitting Subgroups`

  For each selected vertex `Fitting Subgroups` computes and displays its Fitting subgroup. Requires at least one selected vertex. See also FittingSubgroup in the GAP reference manual.

- `Intermediate Subgroups`

  computes and displays all intermediate subgroups between two selected groups. Requires exactly two selected vertices. See also IntermediateSubgroups in the GAP reference manual.

- `Intersection`

  computes and displays the common intersection of the selected vertices. Requires at least one selected vertex. See also Intersection in the GAP reference manual.

- `Intersections`

  For each pair of selected vertices `Intersections` computes and displays the intersection of the two vertices. Requires at least two selected vertices. See also Intersection in the GAP reference manual.

- `Normalizers`

  For each selected vertex `Normalizers` computes and displays its normalizer with respect to the whole group. Requires at least one selected vertex. See also Normalizer in the GAP reference manual.

- `Normal Closures`

  For each selected vertex `Normal Closure` computes and displays its normal closure with respect to the whole group. Requires at least one selected vertex. See also NormalClosure in the GAP reference manual.

- `Normal Subgroups`

  For each selected vertex `Normal Subgroups` computes and displays the normal subgroups of the subgroup associated with this vertex. These new subgroups are not necessarily normal in the whole group. Requires at least one selected vertex. See also NormalSubgroups in the GAP reference manual.

- `Sylow Subgroups`

  pops up a dialog box asking for a prime. After entering a prime p and pressing return or clicking OK it computes and displays a Sylow p-subgroup for each selected vertex. Requires at least one selected vertex. See also SylowSubgroup in the GAP reference manual.

- `SelectedGroups to GAP`

  If the user selects this menu entry, the subgroups belonging to the selected vertices are put into a list which is stored into the variable `last`. This is equivalent to the statement `SelectedGroups(sheet);;` if `sheet` contains the graphic sheet object. If XGAP logging is on, then the normal GAP logging via `LogTo` is also directed to the XGAP log file.

- `InsertVertices from GAP`

  If the user selects this menu entry, the value of the variable `last` is used to insert new vertices into the graphic sheet. If `last` is equal to one subgroup, it is inserted via `InsertVertex`. If `last` is a list of subgroups, `InsertVertex` is called for all those subgroups. There is no error issued if one of the entries of `last` is no subgroup. If XGAP logging is on, then the normal GAP logging via `LogTo` is switched off! The idea of this is to switch the logging temporarily from XGAP logging to normal GAP logging between two clicks to `SelectedGroups to GAP` and `InsertVertices from GAP` respectively.

- `Start Logging`

  After clicking on this menu entry the user is prompted for a filename. From this point on all commands issued via mouse clicks in the subgroup menu are logged into that file, such that one can afterwards see ``what happened'' in the XGAP session. The information displayed is the same as in the info displays in the GAP window.

- `Stop Logging`

  A click onto this menu entry stops the XGAP logging.

  These menu entries represent only a small selection of the functions of GAP which the authors of XGAP considered most frequently used. You can calculate other subgroups like for example prefrattini subgroups from the GAP command window. See sections gapxgap and xgapgap for examples how to transfer information from the graphical lattice of XGAP to GAP (via `SelectedGroups`, see GraphicSubgroupLattice, Selecting Vertices) and vice versa (via `SelectGroups`, see GraphicSubgroupLattice, Selecting Vertices, and `InsertVertex`, see GraphicSubgroupLattice, Inserting Vertices).

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