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Diffstat (limited to 'gap/subgroupladders.gd')
-rw-r--r-- | gap/subgroupladders.gd | 26 |
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diff --git a/gap/subgroupladders.gd b/gap/subgroupladders.gd new file mode 100644 index 0000000..0ba67e9 --- /dev/null +++ b/gap/subgroupladders.gd @@ -0,0 +1,26 @@ +# +# subgroupladders: This package provides an algorithm that computes a subgroup ladder from a permutation group up to the parent symmetric group. +# +# Declarations +# + +#! @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 +DeclareGlobalFunction( "YoungGroupFromPartition" ); +#! @Description +#! Given a permutation group <A>G</A>, this will compute a subgroup ladder +#! from <A>G</A> up to the parent symmetric group. +#! 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>. +#! If <A>G</A> is a Young subgroup of <M>S_n</M>, we can guarantee that all +#! the indices are at most the degree <M>n</M> of the permutation group. +#! Otherwise, we will at first embed <A>G</A> into the Young subgroup +#! corresponding to the orbits of <A>G</A>. +#! At this step, the index may be larger than the degree. +#! @Returns a list of groups +#! @Arguments G +DeclareGlobalFunction( "SubgroupLadder"); |