CARAT Introduction / Programs / Is_finite

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## Program Is_finite

### Usage

    Is_finite 'file1' [-M] [-N] [-o]

file1: bravais_TYP.

### Description

Decides whether the given INTEGRAL matrix group is finite. If it is so, it will echo the order of the group.

### Options

     -M   : Output generators for the Minkowski kernel (i.e the
            subgroup of all matrices congruent I mod 2) of
            the group. WARNING: these generators will be
            correct iff the group was finite. Otherwise
            the program terminates immediatly if it has calculated
            enough element of the kernel to prove the group to
            be infinite.
     -N   : Assume the group to be generated by G->gen, G->normal
            and G->cen.
     -o   : just output the order in a way that can be appended to
            a bravais_TYP.

### Remarks

See also for Order.

### Examples

1. How do the Z-classes in the Q-class of a given group distribute into their Bravais flocks?
2. Do given matrices generate a space group? If so, find its name and normal representation.
3. Is the normalizer of a given group finite?
4. Do two given groups have Z-equivalent copies which lie in a finite unimodular group?

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