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#############################################################################
##
#W irredsol.gd GAP group library Mark Short
#W Burkhard Hofling
##
#H @(#)$Id: irredsol.gd,v 1.6 2002/02/01 16:21:10 gap Exp $
##
#Y Copyright (C) 1993, Murdoch University, Perth, Australia
##
## This file contains the functions and data for the irreducible solvable
## matrix group library. It contains exactly one member for each of the
## 372 conjugacy classes of irreducible solvable subgroups of $GL(n,p)$
## where $1 < n$, $p$ is a prime, and $p^n < 256$.
##
## By well-known theory, this data also doubles as a library of primitive
## solvable permutation groups of non-prime degree $<256$.
##
## This file contains the data from Mark Short's thesis, plus two groups
## missing from that list, subsequently discovered by Alexander Hulpke.
##
Revision.irredsol_gd :=
"@(#)$Id: irredsol.gd,v 1.6 2002/02/01 16:21:10 gap Exp $";
#############################################################################
##
#V IrredSolJSGens[] . . . . . . . . . . . . . . . generators for the groups
##
## 'IrredSolJSGens[<n>][<p>][<k>]' is a generating set for the <k>-th
## JS-maximal of GL(<n>,<p>).
## This generating set is polycyclic, i.e. forms an AG-system for the group.
## A JS-maximal is a maximal irreducible solvable subgroup of GL(<n>,<p>)
## (for a few exceptional small values of n and p this group isn't maximal).
## Every group in the library is generated with reference to the generating
## set of one of these JS-maximals, called its guardian (a group may be a
## subgroup of several JS-maximals but it only has one guardian).
##
DeclareGlobalVariable("IrredSolJSGens");
#############################################################################
##
#V IrredSolGroupList[] . . . . . . . . . . . . . . description of the groups
##
## 'IrredSolGroupList[<n>][<p>][<i>] is a list containing the information
## about the <i>-th group from GL(<n>,<p>).
## The groups are ordered with respect to the following criteria:
## 1. Increasing size
## 2. Increasing guardian number
## If two groups have the same size and guardian, they are in no particular
## order.
##
## The list 'IrredSolGroupList[<n>][<p>][<i>] contains the following info:
## Position: [1]: the size of the group
## [2]: 0 if group is linearly primitive,
## otherwise its minimal block size
## [3]: the absolute value is the number of the group's guardian,
## i.e. its position in 'IrredSolJSGens[<n>][<p>]',
## it's negative iff it equals its guardian
## [4..]: the group's generators in normal form
## (with respect to its guardian's AG-system)
##
DeclareGlobalVariable ("IrredSolGroupList");
#############################################################################
##
#F IrreducibleSolvableGroup( <n>, <p>, <i> )
##
## This function is obsolete, because for $<n> = 2$, $<p> = 13$,
## two groups were missing from the
## underlying database. It has been replaced by the function
## `IrreducibleSolvableGroupMS' (see
## "IrreducibleSolvableGroupMS"). Please note that the latter
## function does not guarantee any ordering of the groups in the database.
## However, for values of <n>, <p>, and <i> admissible to
## `IrreducibleSolvableGroup',
## `IrreducibleSolvableGroupMS' returns a representative of the
## same conjugacy class of subgroups of <GL(n,p)> as
## `IrreducibleSolvableGroup' did before.
##
DeclareGlobalFunction("IrreducibleSolvableGroup");
#############################################################################
##
#F IrreducibleSolvableGroupMS( <n>, <p>, <i> )
##
## This function returns a representative of the <i>-th conjugacy class of
## irreducible solvable subgroup of <GL(n,p)>, where <n> is an
## integer $> 1$, <p> is a prime, and $<p>^{<n>} \< 256$.
##
## The numbering of the representatives should be
## considered arbitrary. However, it is guaranteed that the <i>-th
## group on this list will lie in the same conjugacy class in all future
## versions of {\GAP}, unless two (or more) groups on the list are discovered
## to be duplicates, in which case `IrreducibleSolvableMatrixGroup' will
## return `fail' for all but one of the duplicates.
##
## For values of <n>, <p>, and <i> admissible to `IrreducibleSolvableGroup',
## `IrreducibleSolvableMatrixGroup' returns a representative of the same
## conjugacy class of subgroups of <GL(n,p)> as `IrreducibleSolvableGroup'.
## Note that it currently adds two more groups (missing from the
## original list by Mark Short) for $<n> = 2$, $<p> = 13$.
##
DeclareGlobalFunction("IrreducibleSolvableGroupMS");
#############################################################################
##
#F NumberIrreducibleSolvableGroups( <n>, <p> )
##
## This function returns the number of conjugacy classes of
## irreducible solvable subgroup of
## <GL(n,p)>.
##
DeclareGlobalFunction("NumberIrreducibleSolvableGroups");
DeclareSynonym("NrIrreducibleSolvableGroups",NumberIrreducibleSolvableGroups);
#############################################################################
##
#F AllIrreducibleSolvableGroups( <func_1>, <val_1>, <func_2>, <val_2>, ...)
##
## This function returns a list of conjugacy class representatives <G> of
## matrix groups over a prime field such that $<func_i>(G) = <val_i>$ or
## $<func_i>(G) \in <val_i>$. The following possibilities for <func_i>
## are particularly efficient, because the values can be read off the
## information in the data base: `DegreeOfMatrixGroup' (or
## `Dimension' or `DimensionOfMatrixGroup') for the linear degree,
## `Characteristic' for the field characteristic, `Size',
## `IsPrimitiveMatrixGroup' (or `IsLinearlyPrimitive'), and
## `MinimalBlockDimension'.
##
DeclareGlobalFunction("AllIrreducibleSolvableGroups");
#############################################################################
##
#F OneIrreducibleSolvableGroup( <func1>, <val1>, <func2>, <val2>, ...)
##
## This function returns one solvable subgroup <G> of a
## matrix group over a prime field such that $<func_i>(G) = <val_i>$ or
## $<func_i>(G) \in <val_i>$ for all <i>. The following possibilities
## for <func_i>
## are particularly efficient, because the values can be read off the
## information in the data base: `DegreeOfMatrixGroup' (or
## `Dimension' or `DimensionOfMatrixGroup') for the linear degree,
## `Characteristic' for the field characteristic, `Size',
## `IsPrimitiveMatrixGroup' (or `IsLinearlyPrimitive'), and
## `MinimalBlockDimension'.
##
DeclareGlobalFunction("OneIrreducibleSolvableGroup");
#############################################################################
##
#V DegreeOfMatrixGroup(<G>)
##
## This function returns the dimension of the underlying vector space,
## same as `DimensionOfMatrixGroup'
##
DeclareSynonymAttr ("DegreeOfMatrixGroup", DimensionOfMatrixGroup);
#############################################################################
##
#A MinimalBlockDimension(<G>)
##
## The minimum integer <n> such that the matrix group has an imprimitivity
## system consisting of <n>-dimensional subspaces of the underlying vector
## space over `FieldOfMatrixGroup(G)'
##
DeclareAttribute("MinimalBlockDimension", IsMatrixGroup);
#############################################################################
##
#P IsPrimitiveMatrixGroup(<G>)
##
## `true' if <G> is primitive over `FieldOfMatrixGroup(G)'
##
DeclareProperty("IsPrimitiveMatrixGroup", IsMatrixGroup);
DeclareSynonymAttr ("IsLinearlyPrimitive", IsPrimitiveMatrixGroup);
#############################################################################
##
#E
##
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