51.14 InitPowermap

InitPowermap( tbl, prime )

computes a (probably parametrized, see More about Maps and Parametrized Maps) first approximation of of the prime-th powermap of the character table tbl, using that for any class i of tbl, the following properties hold:

The centralizer order of the image is a multiple of the centralizer order of i. If the element order of i is relative prime to prime, the centralizer orders of i and its image must be equal.

If prime divides the element order x of the class i, the element order of its image must be <x> / <prime>; otherwise the element orders of i and its image must be equal. Of course, this is used only if the element orders are stored on the table.

If no prime-th powermap is possible because of these properties, false is returned. Otherwise InitPowermap returns the parametrized map.

    # cf.\ example in "Powermap"
    gap> t:= CharTable( "U4(3).4" );;
    gap> pow:= InitPowermap( t, 2 );
    [ 1, 1, 3, 4, 5, [ 2, 16 ], [ 2, 16, 17 ], 8, 3, [ 3, 4 ], 
      [ 11, 12 ], [ 11, 12 ], [ 6, 7, 18, 19, 30, 31, 32, 33 ], 14, 
      [ 9, 20 ], 1, 1, 2, 2, 3, [ 3, 4, 5 ], [ 3, 4, 5 ], 
      [ 6, 7, 18, 19, 30, 31, 32, 33 ], 8, 9, 9, [ 9, 10, 20, 21, 22 ], 
      [ 11, 12 ], [ 11, 12 ], 16, 16, [ 2, 16 ], [ 2, 16 ], 17, 17, 
      [ 6, 18, 30, 31, 32, 33 ], [ 6, 18, 30, 31, 32, 33 ], 
      [ 6, 7, 18, 19, 30, 31, 32, 33 ], [ 6, 7, 18, 19, 30, 31, 32, 33 ], 
      20, 20, [ 9, 20 ], [ 9, 20 ], [ 9, 10, 20, 21, 22 ], 
      [ 9, 10, 20, 21, 22 ], 24, 24, [ 15, 25, 26, 40, 41, 42, 43 ], 
      [ 15, 25, 26, 40, 41, 42, 43 ], [ 28, 29 ], [ 28, 29 ], [ 28, 29 ], 
      [ 28, 29 ] ]
    # continued in "Congruences"

InitPowermap is used by Powermap Powermap.

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