ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Tue, 30 Oct 2012 21:46:39 +0100Finding subgroup summandhttps://ask.sagemath.org/question/9484/finding-subgroup-summand/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 " * "Tue, 30 Oct 2012 16:32:49 +0100https://ask.sagemath.org/question/9484/finding-subgroup-summand/Comment by kcrisman for <p>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</p>
<pre><code> D= CyclicPermutationGroup(9)
H=D.subgroups()
for i in H:
for j in H:
i*j=K
if(K==G)
</code></pre>
<p>I have no idea how define " * "</p>
https://ask.sagemath.org/question/9484/finding-subgroup-summand/?comment=18781#post-id-18781http://www.gap-system.org/Manuals/doc/ref/chap49_mj.html suggests this isn't possible even in GAP.Tue, 30 Oct 2012 20:24:28 +0100https://ask.sagemath.org/question/9484/finding-subgroup-summand/?comment=18781#post-id-18781Answer by John Palmieri for <p>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</p>
<pre><code> D= CyclicPermutationGroup(9)
H=D.subgroups()
for i in H:
for j in H:
i*j=K
if(K==G)
</code></pre>
<p>I have no idea how define " * "</p>
https://ask.sagemath.org/question/9484/finding-subgroup-summand/?answer=14214#post-id-14214I 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):
...
Tue, 30 Oct 2012 21:46:39 +0100https://ask.sagemath.org/question/9484/finding-subgroup-summand/?answer=14214#post-id-14214