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| -rw-r--r-- | README.md | 7 | ||||
| -rw-r--r-- | gap/subgroupladders.autodoc | 31 | ||||
| -rw-r--r-- | gap/subgroupladders.gd | 6 |
3 files changed, 38 insertions, 6 deletions
@@ -4,12 +4,12 @@ This package provides an algorithm that computes a subgroup ladder from a permut 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 = H₀,…,Hₖ = Sₙ of the symmetric group Sₙsuch that Hᵢ₋₁ is a subgroup of Hᵢ for every i and transfer the solution of a problem for the symmetric group step by step to G. +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_{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: -A subgroup ladder is series of subgroups G = H₀,…,Hₖ = Sₙ of the symmetric group such that for every 1≤i≤k, Hᵢ is a subgroup of Hᵢ₋₁ or Hᵢ₋₁ is a subgroup of Hᵢ. +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_{i-1} or H_{i-1} 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. @@ -47,6 +47,7 @@ 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 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..2291eb7 100644 --- a/gap/subgroupladders.gd +++ b/gap/subgroupladders.gd @@ -4,14 +4,13 @@ # 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. +#! This function does not check whether the supplied lists are actually disjoint. #! @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 +25,5 @@ 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"); |