GroupTheory`
GroupTheory`

GTQuotientGroup

GTQuotientGroup[group, normal divisor]

] gives the multiplication table of the quotient group of group and its normal divisor.

Details and Options

  • The quotient set of a group and one of its subgroups is formed by the left cosets , , . The quotient set does not form a group.
  • If the quotient set with respect to an invariant subgroup is considered, the quotient set forms a group, the quotient group:
  • If the order of the second group (normal divisor) is larger than that of the first group it is tried to interchange the groups.
  • The following options can be given:
  • GOVerbose TrueControls the output of additional information
    GOQuotientGroup FalseChanges the output of the multiplication table
    GOFast FalseSkips the input validation
  • See: W. Hergert, M. Geilhufe, Group Theory in Solid State Physics and Photonics. Problem Solving with Mathematica, chapter 3.3.

Examples

open allclose all

Basic Examples  (1)

Install groups and .

Test if is an invariant subgroup of .

Construct the quotient group .

Options  (3)

GOVerbose  (1)

Information on invariant subgroup and cosets are giv

Information on invariant subgroup and cosets not provided.

GOQuotientGroup  (1)

Output of the multiplication table of the quotient group.

Output of the quotient group.

GOFast  (1)

Skip the input validation.