GROUP THEORY SYMBOL

GTNormalizer

GTNormalizer[supergroup,group]
constructs the normalizer of a group with respect to its supergroup.

DetailsDetails

  • The normalizer of a group with respect to one of its supergroup consists of the set of elements 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:
  • GOFastGOFastValueControls the input validation

ExamplesExamplesopen allclose all

Basic Examples  (1)Basic Examples  (1)

First load the package:

In[1]:=
Click for copyable input

Install group .

In[2]:=
Click for copyable input
Out[2]=

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

In[3]:=
Click for copyable input
Out[3]=
Out[3]=

The group is the covering group of the group .

In[4]:=
Click for copyable input
Out[4]=

The normalizer is the group .

In[5]:=
Click for copyable input
Out[5]=

is an invariant subgroup of the normalizer.

Top