diff options
author | Ulli Kehrle <ulli.kehrle@rwth-aachen.de> | 2018-11-08 12:46:35 +0100 |
---|---|---|
committer | Ulli Kehrle <ulli.kehrle@rwth-aachen.de> | 2018-11-08 12:46:35 +0100 |
commit | af197de3f2f5581ccfbd1810074dbddd2b3a86a0 (patch) | |
tree | b8190c561fb9bf988ad743eca4c69d588f6e14d3 | |
parent | 893abbaf05ddf0658d8648a3c6f6535708d2e0de (diff) | |
download | subgroup-ladders-af197de3f2f5581ccfbd1810074dbddd2b3a86a0.tar.gz subgroup-ladders-af197de3f2f5581ccfbd1810074dbddd2b3a86a0.tar.xz |
Make documentation more verbose
-rw-r--r-- | gap/subgroupladders.autodoc | 31 | ||||
-rw-r--r-- | gap/subgroupladders.gd | 5 |
2 files changed, 33 insertions, 3 deletions
diff --git a/gap/subgroupladders.autodoc b/gap/subgroupladders.autodoc new file mode 100644 index 0000000..0e9c8d2 --- /dev/null +++ b/gap/subgroupladders.autodoc @@ -0,0 +1,31 @@ +@AutoDocPlainText +@Chapter Introduction + +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 <M>G</M> be a permutation group on the set <M>\{1,...,n\}</M>. +So one might try to find a series of subgroups <M>G = H_0,...,H_k = S_n</M> of the symmetric group <M>S_n</M> such that <M>H_{{i-1}}</M> is a subgroup of <M>H_i</M> for every <M>i</M> and transfer the solution of a problem for the symmetric group step by step to <M>G</M>. + +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 <M>G = H_0,...,H_k = S_n</M> of the symmetric group such that for every <M>1 \leq i \leq k</M>, <M>H_i</M> is a subgroup of <M>H_{{i-1}}</M> or <M>H_{{i-1}}</M> is a subgroup of <M>H_i</M>. +So we sometimes go up to a larger group in order to keep the indices small. + +If <M>G</M> is a Young subgroup of <M>S_n</M>, the algorithm in this repository can find a subgroup ladder of <M>G</M> such that the indices are at most the degree of the permutation group. + +@Chapter subgroupladders +@Section subgroupladders + +@Chapter 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. + +@Chapter References +[1] B. Schmalz. Verwendung von Untergruppenleitern zur Bestimmung von Doppelnebenklassen. Bayreuther Mathematische Schriften, 31, S.109--143, 1990. +@EndAutoDocPlainText diff --git a/gap/subgroupladders.gd b/gap/subgroupladders.gd index 59b9325..b663821 100644 --- a/gap/subgroupladders.gd +++ b/gap/subgroupladders.gd @@ -4,14 +4,12 @@ # Declarations # -#! @Chapter subgroup-ladders -#! @Section subgroup-ladders - #! @Description #! Given a list of lists <A>part</A> of positive integers, this will compute #! the Young subgroup corresponding to this partition. #! @Returns a group #! @Arguments part +#! @ChapterInfo subgroupladders, subgroupladders DeclareGlobalFunction( "YoungGroupFromPartition" ); #! @Description #! Given a permutation group <A>G</A>, this will compute a subgroup ladder @@ -26,4 +24,5 @@ DeclareGlobalFunction( "YoungGroupFromPartition" ); #! At this step, the index may be larger than the degree. #! @Returns a list of groups #! @Arguments G +#! @ChapterInfo subgroupladders, subgroupladders DeclareGlobalFunction( "SubgroupLadder"); |