7.92 DoubleCosets

DoubleCosets( G, U, V )

DoubleCosets returns a list of the double cosets of the subgroups U and V in the group G. The three groups G, U and V must have a common parent. The list is not sorted, i.e., the double cosets may appear in any order. The double cosets are domains as constructed by DoubleCoset (see DoubleCoset).

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

DoubleCosets calls G.operations.DoubleCoset( G, U, V ) and returns that value.

The default function called this way is GroupOps.DoubleCosets, which takes random elements from G, tests if this element lies in one of the already found double cosets, adds the double coset if this is not the case, and continues this until the sum of the sizes of the found double cosets equals the size of G. Look up DoubleCosets in the index, to see for which groups this function is overlaid.

Previous Up Top Next
Index