7.84 RightCosets

Cosets( G, U )
RightCosets( G, U )

Cosets and RightCosets return a list of the right cosets of the subgroup U in the group G. The list is not sorted, i.e., the right cosets may appear in any order. The right cosets are domains as constructed by RightCoset (see RightCoset).

    gap> G := Group( (1,2), (1,2,3,4) );;
    gap> G.name := "G";;
    gap> U := Subgroup( G, [ (1,2), (3,4) ] );;
    gap> RightCosets( G, U );
    [ (Subgroup( G, [ (1,2), (3,4) ] )*()), 
      (Subgroup( G, [ (1,2), (3,4) ] )*(2,4,3)), 
      (Subgroup( G, [ (1,2), (3,4) ] )*(2,3)), 
      (Subgroup( G, [ (1,2), (3,4) ] )*(1,2,4,3)), 
      (Subgroup( G, [ (1,2), (3,4) ] )*(1,2,3)), 
      (Subgroup( G, [ (1,2), (3,4) ] )*(1,3)(2,4)) ] 

If G is the parent of U, the dispatcher RightCosets first checks whether U has a component rightCosets. If U has this component, it returns that value. Otherwise it calls G.operations.RightCosets(G,U), remembers the returned value in U.rightCosets and returns it. If G is not the parent of U, RightCosets directly calls the function G.operations.RightCosets(G,U) and returns that value.

The default function called this way is GroupOps.RightCosets, which calls Orbit( G, RightCoset( U ), OnRight ). Look up RightCosets in the index, to see for which groups this function is overlaid.

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