7.40 JenningsSeries

JenningsSeries( G, p )

JenningsSeries returns the Jennings series of a p-group G.

The Jennings series of a p-group G is defined as follows. S_1 = G and S_n = [ S_{n-1}, G ] {S_i}^p where i is the smallest integer equal or greater than n / p. The length l of S is the smallest integer such that S_l = { 1 }.

Note that S_n = S_{n+1} is possible.

    gap> G := CyclicGroup( AgWords, 27 );
    Group( c27_1, c27_2, c27_3 )
    gap> G.name := "G";;
    gap> JenningsSeries( G );
    [ G, Subgroup( G, [ c27_2, c27_3 ] ), Subgroup( G, [ c27_2, c27_3 ] ),
      Subgroup( G, [ c27_3 ] ), Subgroup( G, [ c27_3 ] ),
      Subgroup( G, [ c27_3 ] ), Subgroup( G, [ c27_3 ] ),
      Subgroup( G, [ c27_3 ] ), Subgroup( G, [ c27_3 ] ),
      Subgroup( G, [  ] ) ] 

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