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author | Ulli Kehrle <ulli.kehrle@rwth-aachen.de> | 2018-11-08 12:04:47 +0100 |
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committer | Ulli Kehrle <ulli.kehrle@rwth-aachen.de> | 2018-11-08 12:04:47 +0100 |
commit | 407bc6af406de7286d377e5f2d1f848aaa84eb2e (patch) | |
tree | 1aa5291f506e9f0b91a7ff0a2e0b70b5e497ba50 /README.md | |
parent | d3d93ebaf723d1c14faaac1062240c8ec7c1bc25 (diff) | |
download | subgroup-ladders-407bc6af406de7286d377e5f2d1f848aaa84eb2e.tar.gz subgroup-ladders-407bc6af406de7286d377e5f2d1f848aaa84eb2e.tar.xz |
use unicode subscripts
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-rw-r--r-- | README.md | 6 |
1 files changed, 3 insertions, 3 deletions
@@ -5,11 +5,11 @@ 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 = H_0,…,H_k = S_n of the symmetric group S_n such 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. +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 Hᵢfor 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 = 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. +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. 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. @@ -38,7 +38,7 @@ A subgroup ladder may look like this: | | H_0 = G -```. +``` TODO: add a description of your package; perhaps also instructions how how to |