GAP:MaximalNormalSubgroups

This article is about a GAP function.

Definition

Function type

The function takes as input an argument representing a group and outputs a list of groups.

Behavior

The function takes as input a group and outputs a list of all its maximal normal subgroups: the subgroups that are maximal among proper normal subgroups. Note that it works only for finite groups.

Specifically:

• If the argument represents a finite group, the function returns a list of its maximal normal subgroups.
• If the argument represents an infinite group, the function returns an error. The nature of the error varies, but it usually involves a memory overflow.
• If the argument is not a group at all, the function returns a NoMethodFound error.

Related functions

• GAP:MaximalSubgroups returns a list of all maximal subgroups. Note that a maximal subgroup need not be a maximal normal subgroup and a maximal normal subgroup need not be a maximal subgroup.
• GAP:ConjugacyClassesMaximalSubgroups returns a list of conjugacy classes of maximal subgroups.
• GAP:MaximalSubgroupClassReps returns a list comprising one member of each conjugacy class of maximal subgroups of the group.