From d3d93ebaf723d1c14faaac1062240c8ec7c1bc25 Mon Sep 17 00:00:00 2001 From: Ulli Kehrle Date: Thu, 8 Nov 2018 11:58:26 +0100 Subject: make this a gap package. --- README.md | 68 ++++++++++++++++++++++++++++++++++++++++++--------------------- 1 file changed, 46 insertions(+), 22 deletions(-) (limited to 'README.md') diff --git a/README.md b/README.md index 48e4066..049e927 100644 --- a/README.md +++ b/README.md @@ -1,10 +1,11 @@ -# subgroup-ladders +# The GAP package subgroupladders -This repository contains a gap implementation of an algorithm described by Bernd Schmalz [1, Theorem 3.1.1] to compute subgroup ladders of permutation groups. +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 of subgroups G = H_0,…,H_k = S_n of the symmetric group S_n such that H_{i-1} 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. +So one might try to find a series of subgroups G = H_0,…,H_k = S_n of the symmetric group S_n such that H_{i-1} 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: @@ -12,27 +13,50 @@ A subgroup ladder is series of subgroups G = H_0,…,H_k = S_n of the symmetric 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 -S_n - | - | - | -H_1 - | H_3 - | /| - | / | - | / | -H_2 | - H_4 - | H_6 - | / | - | / | - | / | - H_5 | - | - H_7 = G -``` + 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 + + +## Contact + +You can report issues on GitHub at . + + +## 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 -- cgit v1.2.3-24-g4f1b