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Finding subgroup summand

asked 2012-10-30 16:32:49 +0200

Babgen gravatar image

updated 2012-10-30 16:33:45 +0200

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 20:24:28 +0200 )edit

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answered 2012-10-30 21:46:39 +0200

updated 2012-10-30 23:01:33 +0200

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 16:32:49 +0200

Seen: 92 times

Last updated: Oct 30 '12