Math.Algebra.Group.Subquotients

Documentation

isLeft :: Either a b -> Bool

isRight :: Either a b -> Bool

unRight :: Ord a1 => Permutation (Either a2 a1) -> Permutation a1

restrictLeft :: Ord a => Permutation (Either a b) -> Permutation a

ptStab :: (Show a, Foldable t, Ord a) => [Permutation a] -> t a -> [Permutation a]

isTransitive :: Ord t => [Permutation t] -> Bool

transitiveConstituentHomomorphism :: (Ord a, Show a) => [Permutation a] -> [a] -> ([Permutation a], [Permutation a])

Given a group gs and a transitive constituent ys, return the kernel and image of the transitive constituent homomorphism. That is, suppose that gs acts on a set xs, and ys is a subset of xs on which gs acts transitively. Then the transitive constituent homomorphism is the restriction of the action of gs to an action on the ys.

transitiveConstituentHomomorphism' :: (Foldable t, Show b, Ord b) => [Permutation b] -> t b -> ([Permutation b], [Permutation b])

minimalBlock :: Ord a => [Permutation a] -> [a] -> [[a]]

blockSystems :: Ord t => [Permutation t] -> [[[t]]]

Given a transitive group gs, find all non-trivial block systems. That is, if gs act on xs, find all the ways that the xs can be divided into blocks, such that the gs also have a permutation action on the blocks

blockSystemsSGS :: Ord a => [Permutation a] -> [[[a]]]

A more efficient version of blockSystems, if we have an sgs

isPrimitive :: Ord t => [Permutation t] -> Bool

A permutation group is primitive if it has no non-trivial block systems

isPrimitiveSGS :: Ord a => [Permutation a] -> Bool

blockHomomorphism :: (Ord t, Show t) => [Permutation t] -> [[t]] -> ([Permutation t], [Permutation [t]])

Given a transitive group gs, and a block system for gs, return the kernel and image of the block homomorphism (the homomorphism onto the action of gs on the blocks)

blockHomomorphism' :: (Show b, Ord b) => [Permutation b] -> [[b]] -> ([Permutation b], [Permutation [b]])

normalClosure :: (Show a, Ord a) => [Permutation a] -> [Permutation a] -> [Permutation a]

intersectionNormalClosure :: (Show a, Ord a) => [Permutation a] -> [Permutation a] -> [Permutation a]

centralizerSymTrans :: (Show a, Ord a) => [Permutation a] -> [Permutation a]