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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

Calling Sequence

cosets(sbgrl)

cosets(pg, sbpg)

Parameters

sbgrl

-

subgroup of a group given by generators and relations

pg, sbpg

-

permutation groups of same degree

Description

• 

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.

Examples

Important: The group package has been deprecated. Use the superseding command GroupTheory[RightCosets] instead.

withgroup:

g:=grelgroupa,b,c,a,b,c,a,1b,b,c,a,b,1c,c,a,b,c,1a:

cosetssubgrely=a,b,c,g

,a,a,b

(1)

pg1:=permgroup7,1,2,1,2,3,4,5,6,7:

pg2:=permgroup7,1,2,3,3,4,5,6,7:

cosetspg1,pg2

,6,7

(2)

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:=permgroup4,1,2,1,4:

ident:=permgroup4,:

cosetspg,ident

,1,2,1,4,2,4,1,2,4,1,4,2

(3)

See Also

group[grelgroup], group[permgroup], group[subgrel], GroupTheory, GroupTheory[RightCosets]


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