find a complete list of right coset representatives for a subgroup of a permutation group or a group given by generators and relations
subgroup of a group given by generators and relations
permutation groups of same degree
Important: The group package has been deprecated. Use the superseding command GroupTheory[RightCosets] instead.
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.
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.
The command with(group,cosets) allows the use of the abbreviated form of this command.
g ≔ grelgroup⁡a,b,c,a,b,c,a,1b,b,c,a,b,1c,c,a,b,c,1a:
pg1 ≔ permgroup⁡7,1,2,1,2,3,4,5,6,7:
pg2 ≔ permgroup⁡7,1,2,3,3,4,5,6,7:
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:
pg ≔ permgroup⁡4,1,2,1,4:
ident ≔ permgroup⁡4,:
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