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Topic: Let G be a group , N a normal subgroup of G
Replies: 13   Last Post: Feb 6, 2013 6:11 AM

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 dan.ms.chaos@gmail.com Posts: 409 Registered: 3/1/08
Re: Yes
Posted: Feb 5, 2013 1:03 PM

On Feb 5, 6:34 pm, Bart Goddard <goddar...@netscape.net> wrote:
> Dan <dan.ms.ch...@gmail.com> wrote in news:43bcf432-0c9a-41e2-9eea-
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> > On Feb 5, 4:24 pm, Robin Chapman <R.J.Chap...@ex.ac.uk> wrote:
> >> On 05/02/2013 14:08, Dan wrote:
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> >> > On Feb 5, 3:45 pm, Robin Chapman <R.J.Chap...@ex.ac.uk> wrote:
> >> >> On 05/02/2013 13:27, Dan wrote:
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> >> >>> Does there always exist a subgroup H of G such that G = NH , and
> >> >>> (H intersection N) = the identity element?

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> >> > Can you provide an example?
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> > Fun fact :If the set of possible answers is infinite , and person T (T
> > stands for troll) claims to have one ,then person B cannot determine
> > for sure using only yes or no questions . Each question is a function
> > from the set of remaining answers to {Yes,No} . Provided that the set
> > is infinite , either the inverse image to Yes or the inverse image of
> > No is infinite . There exists a sequence of choices as answers of T
> > such that the set of 'remaining valid answers' always remains
> > infinite , thereby always giving the impression of knowledge of an
> > answer ,  while ensuring for a fact that such an answer does not
> > exist .

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> That's an interesting alternative universe you've got there.  Something
> closer to reality would be that person T (T for teacher) doesn't want to
> do your homework for you, but was helpful enough to tell you the right
> answer, so that you wouldn't waste a lot of time looking for a proof
> rather than a counter-example.  I'm surprised you aren't more grateful.
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> B.

'Z4' is two characters that would have been a sufficient answer .My
fault , indeed , lies is not being able to see it. It's not a homework
question , I simply thought of it while studying semi-direct products.
I will admit to stupidity , not malice , though I preferred it be the
other way around , then I wouldn't be asking the question .