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# The GAP package subgroupladders
This package provides an algorithm that computes a subgroup ladder from a permutation group up to the parent symmetric group.
The algorithm was described by Bernd Schmalz in [1, Theorem 3.1.1].
Solutions of some problems in group theory can relatively easy be transferred to a sub or supergroup if the index is small.
Let G be a permutation group on the set {1,...,n}.
So one might try to find a series of subgroups G = H_0,...,H_k = S_n of the symmetric group S_nsuch that H_{i1} is a subgroup of H_i for every i and transfer the solution of a problem for the symmetric group step by step to G.
Sometimes it is not possible to find such a series with small indices between consecutive subgroups.
This is where subgroup ladders may make sense:
A subgroup ladder is series of subgroups G = H_0,...,H_k = S_n of the symmetric group such that for every 1<=i<=k, H_i is a subgroup of H_{i1} or H_{i1} is a subgroup of H_i.
So we sometimes go up to a larger group in order to keep the indices small.
If G is a Young subgroup of S_n, the algorithm in this repository can find a subgroup ladder of G such that the indices are at most the degree of the permutation group.
A subgroup ladder may look like this:
```text
H_8 = S_n



H_7
 H_5
 /
 / 
 / 
H_6 
H_4
 H_2
 / 
 / 
 / 
H_3 

H_1



H_0 = G
```
TODO: add a description of your package; perhaps also instructions how how to
install and use it, resp. where to find out more
## Documentation
The documentation of this package is available as [HTML](https://hrnz.li/subgroupladders) and as a [PDF](https://hrnz.li/subgroupladders/manual.pdf).
It can also be generated locally with `gap makedoc.g`.
## Contact
You can report issues on GitHub at <https://github.com/ehwat/subgroupladders>.
## License
subgroupladders is free software you can redistribute it and/or modify it under
the terms of the GNU General Public License as published by the Free Software
Foundation; either version 3 of the License, or (at your option) any later
version. For details, see the file LICENSE distributed as part of this package
or see the FSF's own site.
## References
[1] B. Schmalz. Verwendung von Untergruppenleitern zur Bestimmung von Doppelnebenklassen. Bayreuther Mathematische Schriften, 31, S.109143, 1990.
