[GAP Forum] First set in RightCosets

[Alexander Hulpke]

Dear Forum, Dear Ivo Hedtke,

> can I assume, that the first set in SG:=RightCosets(G,S) is the set S itself, or is it possible, that SG[1] is not S?

At this point this seems to be the case for all methods installed. However one of them is an `Orbit' computation and `Orbit' explicitly *disclaims* that any particular ordering will be returned. Thus I am rather reluctant to introduce such a condition for RightCosets (or `RightTransversal').

Code that requires the position of the trivial coset would need to test first, I would use the following snippet:

trivialcoset:=PositionProperty(SG,x->One(G) in x);    # since it very often will be in the first position this does not take long.
indicesother:=Difference([1..Length(SG)],[trivialcoset]); # index set for running over the other cosets.

Best,

  Alexander Hulpke



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