[xgap] 5.13 GraphicSubgroupLattice for FpGroups, Information Menu

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# 5.13 GraphicSubgroupLattice for FpGroups, Information Menu

Placing the pointer inside a vertex (selected or not) and pressing the right mouse button pops up the ``Information'' menu. Clicking on any of the text lines will compute the corresponding property of the subgroup u associated with this vertex. Clicking on `close` will close the ``Information'' menu.

- `Index`

  displays the index of u in the whole group.

- `IsNormal`

  checks if u is normal in the whole group.

- `IsFpGroup`

  checks if u is a finitely presented group. Note that a subgroup of a finitely presented group that is defined by a coset table or as kernel of an epimorphism is not automatically known to GAP as a finitely presented group. This means, that certain algorithms can not be applied. Use `IsomorphismFpGroup` (see IsomorphismFpGroup in the GAP reference manual) to calculate a finitely presented group and an isomorphism onto it, if some calculation does not work automatically.

- `Abelian Invariants`

  computes and displays the abelian invariants of u.

- `Coset Table`

  computes a coset table for u.

- `IsomorphismFpGroup`

  computes a finitely presented group that is isomorphic to u and displays the number of generators and relators of it.

- `Factor Fp Group`

  computes the factor group of the whole group by u, if u is normal.

  Note that the exact result of all these information displays is stored in the global variable `LastResultOfInfoDisplay` after each operation. So you can access this easily from the GAP command prompt. It is also returned as `last` value.

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