## RCWA

### Summary

RCWA is a package for the computer algebra system GAP.

It provides implementations of algorithms and methods for computing

in certain infinite permutation groups.

The class of groups which RCWA in principle can deal with includes

the finite groups, the free groups of finite rank, the free products

of finitely many finite groups, certain infinite simple groups,

certain divisible torsion groups and groups of many further types.

It is closed under taking direct products and under taking wreath

products with finite groups and with the infinite cyclic group (Z,+).

### Authors

Stefan Kohl

### Vendor

RCWA is free software. It is distributed by the author and redistributed by the GAP Group.

### Status

officially approved by the authors### Aims and scope

### Mathematical Classification

### Keywords

- 3n+1 conjecture
- collatz conjecture
- Collatz mapping
- combinatorial group theory
- direct products
- extracting roots of rcwa mappings
- factoring Collatz' permutation
- factoring rcwa permutations
- finite groups
- free groups
- free groups of finite rank
- geometric group theory
- Grigorchuk groups
- group actions
- group elements
- group of rcwa permutations of a ring
- group products
- group properties
- group representations
- groups
- group theory
- infinite groups
- infinite permutation groups
- monoid of rcwa mappings of a ring
- multiply transitive infinite permutation groups
- number theory
- orbits
- permutation groups
- permutations
- preimages in the free group
- rcwa groups
- rcwa mappings
- residue classes
- residue-class-wise affine groups
- residue-class-wise affine mappings
- signs of rcwa permutations of Z
- subgroups
- torsion groups
- trajectories and cycles of rcwa mappings
- transition graphs
- transition matrices
- transitive permutation groups
- vector spaces
- wreath products