GroupTheory`
GroupTheory`

GTNormalizer

GTNormalizer[supergroup,group]

constructs the normalizer of a group with respect to its supergroup.

Details and Options

  • The normalizer of a group with respect to one of its supergroups consists of the set of elements of mapping the group onto itself.
  • If the order of group is larger than the order of supergroup, both groups will be interchanged.
  • The following option can be given:
  • GOFast GOFastValueControls the input validation

Examples

open allclose all

Basic Examples  (1)

First load the package:

Install group .

Find all subgroups and take one group, e.g., .

The group is the covering group of the group .

The normalizer is the group .

is an invariant subgroup of the normalizer.

Options  (1)

GOFast  (1)

The evaluation time can be decreased, using GOFastTrue.

Not every time you ill really benefit from this option.