As for all domains (see Domains and Domain Records) groups and their
subgroups are represented by records that contain important information
about groups. Most of the following functions return such records. Of
course it is possible to create a group record by hand but generally
Group (see Group) and
Subgroup (see Subgroup) should be used for
Once a group record is created you may add record components to it but
you must not alter informations already present, especially not
Group records must always contain the components
isGroup. Subgroups contain an additional
parent. The contents of all components of a group G are
The following two components are the so-called category components used to identify the category this domain belongs to.
trueas a group is a domain.
trueas G is a group.
The following three components determine a group domain. These are the so-called identification components.
generatorsis the empty list. Note that once created this entry must never be changed, as most of the other entries depend on
The following components are optional and contain knowledge about the group G.
G.lattice.classes, contains the conjugacy classes of subgroups of G. See ConjugacyClassesSubgroups.
The following components are
true if the group G has the property,
false if not, and are not present if it is unknown whether the group
has the property or not.
trueif the group G is abelian. See IsAbelian.
trueif the group G is central in its parent group. See IsCentral.
trueif the group G is cyclic. See IsCyclic.
trueif the group G is elementary abelian. See IsElementaryAbelian.
trueif the group G is finite. If you know that a group for which you want to use the generic low level group functions is infinite, you should set this component to
false. This will avoid attempts to compute the set of elements.
trueif the group G is nilpotent. See IsNilpotent.
trueif the group G is normal in its parent group. See IsNormal.
trueif the group G is perfect. See IsPerfect.
trueif the group G is simple. See IsSimple.
trueif the group G is solvable. See IsSolvable.
trueif the group G is subnormal in its parent group. See IsSubnormal.
Domain Records and Dispatchers).
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