> < ^ From:

< ^ Subject:

Dear Gap-Forum,

Javaid Aslam asked:

I am searching for possibly a gap implementation of:

double coset reprensentatives of subgroups (say) H and K

in a permutation group G.

The operation `DoubleCosets(G,U,V)' will compute double cosets U\G/V.

At the moment the method used for permutation groups is the generic method

provided by `CalcDoubleCosets' (in lib/csetgrp.gi). Permutation specific code

then gets executed in the operations called to determine subgroup chains and

identify right cosets.

Also if somebody can provide some guidelines on how to determine

a canonical representative of the coset HgK, where g is a member of G.

The operation `CanonicalRightCosetElement' will return the lexicographical

smallest element of the right coset Hg. By having K act on right coset

representatives by right multiplication, canonizing each multiplication

result, one obtains canonical representatives for all right cosets of H

contained in HgK.

In GAP this is provided by the operation `RepresentativesContainedRightCosets'.

One could define the smallest of these representatives to be the canonical

representative for HgK.

(G. Butler (On computing double coset representatives in permutation groups.

Computational group theory, 283--290, Academic Press) suggests to use these

representatives to actually compute double cosets, the approach used by

GAP seems to be more deterministic.)

I hope this is of help,

Alexander Hulpke

-- The Ohio State University, Department of Mathematics,

231W 18th Avenue, Columbus, OH 43210, USA

email: ahulpke@math.ohio-state.edu, Phone: ++1-614-688-3175

> < [top]