GROUP THEORY SYMBOL

GTProductGroupQ

GTProductGroupQ[group,group1,group2]
gives True if group is a product group of the groups group1 and group2, and False otherwise.

DetailsDetails

  • First it is checked, if group1 and group2 are subgroups of group . Furthermore it is tested that group1 and group2 have only the element in common. In an next step it is tested, if the product of group1 and group2 is really a group. After the check of all suppositions it is finally checked if the product is a product group or a semi-direct product group.
  • The following options can be given:
  • GOFastGOFastValueControls the input validation
    GOVerboseFalseControls the output of additional information

ExamplesExamplesopen allclose all

Basic Examples  (1)Basic Examples  (1)

First load the package:

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The group will be installed and checked which subgroups and invariant subgroups exist.

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Now the construction of as a product can be checked.

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Find the positions of the invariant subgroups in sgr.

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Which product of subgroups gives the group ?

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Options  (2)Options  (2)

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