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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