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authorUlli Kehrle <ulli.kehrle@rwth-aachen.de>2018-11-08 12:26:01 +0100
committerUlli Kehrle <ulli.kehrle@rwth-aachen.de>2018-11-08 12:26:01 +0100
commit893abbaf05ddf0658d8648a3c6f6535708d2e0de (patch)
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parentc6d6742b3eaef6370e47a4cc7e329ec5c734aacc (diff)
downloadsubgroup-ladders-893abbaf05ddf0658d8648a3c6f6535708d2e0de.tar.gz
subgroup-ladders-893abbaf05ddf0658d8648a3c6f6535708d2e0de.tar.xz
Don't use unicode subscripts in README as some systems don't render it properly.
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@@ -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 = Sₙ 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.