group[cosets] - find a complete list of right coset representatives for a subgroup of a permutation group or a group given by generators and relations
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Calling Sequence
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cosets(sbgrl)
cosets(pg, sbpg)
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Parameters
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sbgrl
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subgroup of a group given by generators and relations
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pg, sbpg
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-
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permutation groups of same degree
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Description
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For groups given by generators and relations, the argument sbgrl should be a subgrel. A set of words in the generators of the group is returned.
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For permutation groups, both arguments should be permgroups and sg should be a subgroup of pg. A set of permutations in disjoint cycle notation is returned.
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The command with(group,cosets) allows the use of the abbreviated form of this command.
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Examples
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The cosets function can be used to produce all of the elements of a group by finding the cosets of the identity element of the group:
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