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diff --git a/gap/subgroupladders.autodoc b/gap/subgroupladders.autodoc new file mode 100644 index 0000000..0e9c8d2 --- /dev/null +++ b/gap/subgroupladders.autodoc @@ -0,0 +1,31 @@ +@AutoDocPlainText +@Chapter Introduction + +This package provides an algorithm that computes a subgroup ladder from a permutation group up to the parent symmetric group. +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 <M>G</M> be a permutation group on the set <M>\{1,...,n\}</M>. +So one might try to find a series of subgroups <M>G = H_0,...,H_k = S_n</M> of the symmetric group <M>S_n</M> such that <M>H_{{i-1}}</M> is a subgroup of <M>H_i</M> for every <M>i</M> and transfer the solution of a problem for the symmetric group step by step to <M>G</M>. + +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 <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>. +So we sometimes go up to a larger group in order to keep the indices small. + +If <M>G</M> is a Young subgroup of <M>S_n</M>, the algorithm in this repository can find a subgroup ladder of <M>G</M> such that the indices are at most the degree of the permutation group. + +@Chapter subgroupladders +@Section subgroupladders + +@Chapter License + +subgroupladders is free software you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free Software +Foundation; either version 3 of the License, or (at your option) any later +version. For details, see the file LICENSE distributed as part of this package +or see the FSF's own site. + +@Chapter References +[1] B. Schmalz. Verwendung von Untergruppenleitern zur Bestimmung von Doppelnebenklassen. Bayreuther Mathematische Schriften, 31, S.109--143, 1990. +@EndAutoDocPlainText |