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Finding subgroup summand

asked 2012-10-30 10:32:49 -0500

Babgen gravatar image

updated 2012-10-30 10:33:45 -0500

Hi everyone, Let (G,.) be group with two subgroup H and K, I want to know when HK=G? $HK={h.k | h\in H ,k\in K}$ I try this

  D= CyclicPermutationGroup(9)
  H=D.subgroups()
  for i in H:
   for j in H:
     i*j=K
   if(K==G)

I have no idea how define " * "

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http://www.gap-system.org/Manuals/doc/ref/chap49_mj.html suggests this isn't possible even in GAP.

kcrisman gravatar imagekcrisman ( 2012-10-30 14:24:28 -0500 )edit

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answered 2012-10-30 15:46:39 -0500

updated 2012-10-30 17:01:33 -0500

I suppose you can try this:

D = CyclicPermutationGroup(9)
H = D.subgroups()
for i in H:
    for j in H:
        K = set(D(x*y) for x in i for y in j)
        if K == set(D):
            ...
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Asked: 2012-10-30 10:32:49 -0500

Seen: 65 times

Last updated: Oct 30 '12