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author | Ulli Kehrle <ulli.kehrle@rwth-aachen.de> | 2018-11-08 12:26:01 +0100 |
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committer | Ulli Kehrle <ulli.kehrle@rwth-aachen.de> | 2018-11-08 12:26:01 +0100 |

commit | 893abbaf05ddf0658d8648a3c6f6535708d2e0de (patch) | |

tree | cb2f52156527373f3b17fe9e4513dc5b1b1962d3 | |

parent | c6d6742b3eaef6370e47a4cc7e329ec5c734aacc (diff) | |

download | subgroup-ladders-893abbaf05ddf0658d8648a3c6f6535708d2e0de.tar.gz subgroup-ladders-893abbaf05ddf0658d8648a3c6f6535708d2e0de.tar.xz |

Don't use unicode subscripts in README as some systems don't render it properly.

This mostly reverts 407bc6af406de7286d377e5f2d1f848aaa84eb2e.

-rw-r--r-- | README.md | 6 |

1 files changed, 3 insertions, 3 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 = 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. |